Event-triggered mixed <inline-formula><tex-math id="M1">\begin{document}$ H_\infty $\end{document}</tex-math></inline-formula> and passive control for Markov jump systems with bounded inputs

Liqiang Jin; Yanyan Yin; Kok Lay Teo; Fei Liu

doi:10.3934/jimo.2020024

Previous Article
New inertial method for generalized split variational inclusion problems
JIMO Home
This Issue
Next Article
Time-consistent strategy for a multi-period mean-variance asset-liability management problem with stochastic interest rate

doi: 10.3934/jimo.2020024

Event-triggered mixed $ H_\infty $ and passive control for Markov jump systems with bounded inputs

Liqiang Jin ^1, , Yanyan Yin ^2, , Kok Lay Teo ^2,3, and Fei Liu ^1,,

1.	Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Institute of Automation, School of Internet of Things Engineering, Jiangnan University, Wuxi, 214122, China
2.	School of Electrical Engineering, Computing and Mathematical Sciences, Curtin University, Perth, Western Australia, 6102, Australia
3.	Coordinated Innovation Center for Computable Modeling in Management Science, Tianjin University of Finance and Economics, Tianjin, China

^* Corresponding author: Fei Liu

Received November 2018 Revised August 2019 Published February 2020

Fund Project: The first author is supported in part by the National Natural Science Foundation of China under grant nos. 61773011, 61773183, NSFC 61833007, the Ministry of Education of China under the 111 Project B12018 and Curtin Fellowship

In this brief, the problem of event-triggered mixed $ {H_\infty } $ and passive control for a class of discrete-time stochastic Markov jump systems with bounded inputs is addressed. In order to reduce the frequency of the variation of the controller, an effective triggered scheme, called event-triggered scheme, is proposed, where unlike the traditional triggered scheme, not all sampling states are required to be transmitted to the controller. The event-triggered controller, which is designed using Lyapunov functional analysis approach and slack matrices, can ensure that the resulting system is stochastically stable with a prescribed mixed $ {H_\infty } $ and passive performance index. Sufficient conditions in terms of linear matrix inequalities (LMIs) are derived. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

Keywords: Event-triggered, mixed $ {H_\infty } $ and passive control, Markov jump systems, input constraints.

Mathematics Subject Classification: Primary: 93C55, 93C65; Secondary: 37C75.

Citation: Liqiang Jin, Yanyan Yin, Kok Lay Teo, Fei Liu. Event-triggered mixed $ H_\infty $ and passive control for Markov jump systems with bounded inputs. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2020024

References:

[1]	P. Bolzern, P. Colaneri and G. De Nicolao, Stochastic stability of positive Markov jump linear systems, Automatica, 50 (2014), 1181-1187. doi: 10.1016/j.automatica.2014.02.016. Google Scholar
[2]	X. H. Chang and G. H. Yang, New results on output feedback $H_\infty$ control for linear discrete-time systems, IEEE Transactions on Automatic Control, 59 (2014), 1355-1359. doi: 10.1109/TAC.2013.2289706. Google Scholar
[3]	J. Cheng, J. H. Park, L. Zhang and Y. Zhu, An asynchronous operation approach to event-triggered control for fuzzy Markovian jump systems with general switching policies, IEEE Transactions on Fuzzy Systems, 26 (2018), 6-18. doi: 10.1109/TFUZZ.2016.2633325. Google Scholar
[4]	D. V. Dimarogonas, E. Frazzoli and K. H. Johansson, Distributed event-triggered control for multi-agent systems, IEEE Transactions on Automatic Control, 57 (2012), 1291-1297. doi: 10.1109/TAC.2011.2174666. Google Scholar
[5]	H. Dong, Z. Wang, D. W. C. Ho and H. Gao, Robust $ H_{\infty} $ Filtering for Markovian Jump Systems With Randomly Occurring Nonlinearities and Sensor Saturation: The Finite-Horizon Case, IEEE Transactions on Signal Processing, 59 (2011), 3048-3057. doi: 10.1109/TSP.2011.2135854. Google Scholar
[6]	Y. Dong, E. Tian and Q. L. Han, A delay system method for designing event-triggered controllers of networked control systems, IEEE Transactions on Automatic Control, 58 (2013), 475-481. doi: 10.1109/TAC.2012.2206694. Google Scholar
[7]	S. He, Non-fragile passive controller design for nonlinear Markovian jumping systems via observer-based controls, Neurocomputing, 147 (2015), 350-357. doi: 10.1016/j.neucom.2014.06.053. Google Scholar
[8]	W. P. M. H. Heemels, M. C. F. Donkers and A. R. Teel, Periodic event-triggered control for linear systems, IEEE Transactions on Automatic Control, 58 (2013), 847-861. doi: 10.1109/TAC.2012.2220443. Google Scholar
[9]	F. Li, P. Lim, C. C. Shi and L. Wu, Fault detection filtering for nonhomogeneous Markovian jump systems via fuzzy approach, IEEE Transactions on Fuzzy Systems, 26 (2018), 131-141. doi: 10.1109/TFUZZ.2016.2641022. Google Scholar
[10]	H. Li, Z. Chen, L. Wu, H. K. Lam and H Du, Event-triggered fault detection of nonlinear networked systems, IEEE Transactions on Cybernetics, 47 (2017), 1041-1052. doi: 10.1109/TCYB.2016.2536750. Google Scholar
[11]	H. Li, Y. Wang, D. Yao and R. Lu, A sliding mode approach to stabilization of nonlinear Markovian jump singularly perturbed systems, Automatic, 97 (2018), 404-413. doi: 10.1016/j.automatica.2018.03.066. Google Scholar
[12]	H. Liang, L. Zhang, H. R. Karimi and Q. Zhou, Fault estimation for a class of nonlinear sem-Markovian jump systems with partly unknown transition rates and output quantization, International Journal of Robust and Nonlinear Control, 28 (2018), 5962-5980. doi: 10.1002/rnc.4353. Google Scholar
[13]	M. Liu, D. W. C. Ho and P. Shi, Adaptive fault-tolerant compensation control for Markovian jump systems with mismatched external disturbance, Automatic, 58 (2015), 5-14. doi: 10.1016/j.automatica.2015.04.022. Google Scholar
[14]	Y. Liu, Y. Yin, K. L. Teo, S. Wang and F. Liu, Probabilistic control of Markov jump systems by scenario optimization approach, Journal of Industrial and Management Optimization, 15 (2019), 1447-1453. doi: 10.3934/jimo.2018103. Google Scholar
[15]	S. Ma and E. K. Boukas, A singular system approach to robust sliding mode control for uncertain Markov jump systems, Automatica, 45 (2009), 2707-2713. doi: 10.1016/j.automatica.2009.07.027. Google Scholar
[16]	M. Mariton, Jump Linear Systems in Automatic Control, New York: M. Dekker, 1990. Google Scholar
[17]	N. Meskin and K. Khorasani, Fault detection and isolation of discrete-time Markovian jump linear systems with application to a network of multi-agent systems having imperfect communication channels, Automatic, 45 (2009), 2032-2040. doi: 10.1016/j.automatica.2009.04.020. Google Scholar
[18]	C. Peng and T. C. Yang, Event-triggered communication and ${H_\infty }$ control co-design for networked control systems, Automatic, 49 (2013), 1326-1332. doi: 10.1016/j.automatica.2013.01.038. Google Scholar
[19]	P. Shi, Y. Zhang, M. Chadli and R. X. Agarwal, Mixed H-infinity and passive filtering for discrete fuzzy neural networks with stochastic jumps and time delays, IEEE Transactions on Neural Networks and Learning Systems, 27 (2016), 903-909. doi: 10.1109/TNNLS.2015.2425962. Google Scholar
[20]	Z. Wang, Y. Liu and X. Liu, Exponential stabilization of a class of stochastic system with Markovian jump parameters and mode-dependent mixed time-delays, IEEE Transactions on Automatic Control, 55 (2010), 1656-1662. doi: 10.1109/TAC.2010.2046114. Google Scholar
[21]	L. Wu, P. Shi, H. Gao and C. Wang, ${H_\infty }$ filtering for 2D Markovian jump systems, Automatic, 44 (2008), 1849-1858. doi: 10.1016/j.automatica.2007.10.027. Google Scholar
[22]	L. Wu, X. Yao and W. X. Zheng, Generalized ${H_2 }$ fault detection for two-dimensional Markovian jump systems, Automatic, 48 (2012), 1741-1750. doi: 10.1016/j.automatica.2012.05.024. Google Scholar
[23]	Z. G. Wu, P. Shi, Z. Shu, H. Su and R. Lu, Passivity-based asynchronous control for Markov jump systems, IEEE Transactions on Automatic Control, 62 (2017), 2020-2025. doi: 10.1109/TAC.2016.2593742. Google Scholar
[24]	S. Xu, T. Chen and J. Lam, Robust ${H_\infty }$ filtering for uncertain Markovian jump systems with mode-dependent time delays, IEEE Transactions on Automatic Control, 48 (2003), 900-907. doi: 10.1109/TAC.2003.811277. Google Scholar
[25]	Y. Yin and Z. Lin, Constrained control of uncertain nonhomogeneous Markovian jump systems, International Journal of Robust and Nonlinear Control, 27 (2017), 3937-3950. Google Scholar
[26]	Y. Yin, Y. Liu, K. L. Teo and S. Wang, Event-triggered probabilistic robust control of linear systems with input constrains: By scenario optimization approach, International Journal of Robust and Nonlinear Control, 28 (2018), 144-153. doi: 10.1002/rnc.3858. Google Scholar
[27]	S. Yu, T. Qu, F. Xu, H. Chen and Y. Hu, Stability of finite horizon model predictive control with incremental input constraints, Automatic, 79 (2017), 265-272. doi: 10.1016/j.automatica.2017.01.040. Google Scholar
[28]	H. Zhang, Y. Shi and J. Wang, On energy-to-peak filtering for nonuniformly sampled nonlinear systems: A Markovian jump system approach, IEEE Transactions on Fuzzy Systems, 22 (2014), 212-222. doi: 10.1109/TFUZZ.2013.2250291. Google Scholar
[29]	X. Zhao, X. Zheng, D. Yao and L. Wu, Adaptive tracking control for a class of uncertain switched nonlinear systems, Automatica, 52 (2015), 185-191. doi: 10.1016/j.automatica.2014.11.019. Google Scholar
[30]	H. Zhang, G. Zhang and J. Wang, $H_\infty$ observer design for LPV systems with uncertain measurements on scheduling variables: application to an electric ground vehicle, IEEE/ASME Transactions on Mechatronics, 21 (2016), 1659-1670. doi: 10.1109/TMECH.2016.2522759. Google Scholar
[31]	H. Zhang and J. Wang, Active steering actuator fault detection for an automatically-steered electric ground vehicle, IEEE Transactions on Vehicular Technology, 66 (2016), 3685-3702. doi: 10.1109/TVT.2016.2604759. Google Scholar
[32]	M. Zhang, P. Shi, L. Ma, J. Cai and H. Su, Network-based fuzzy control for nonlinear Markov jump systems subject to quantization and dropout compensation, Fuzzy Sets and Systems, 371 (2019), 96-109. doi: 10.1016/j.fss.2018.09.007. Google Scholar
[33]	L. Zhang, ${H_\infty }$ estimation for discrete-time piecewise homogeneous Markov jump linear systems, Automatic, 45 (2009), 2570-2576. doi: 10.1016/j.automatica.2009.07.004. Google Scholar
[34]	X. M. Zhang and Q. L. Han, Event-based ${H_\infty }$ filtering for sampled-data systems, Automatica, 51 (2015), 55-69. doi: 10.1016/j.automatica.2014.10.092. Google Scholar
[35]	Y. Zhang, Y. He, M. Wu and J. Zhang, Stabilization for Markovian jump systems with partial information on transition probability based on free-connection weighting matrices, Automatica, 47 (2011), 79-84. doi: 10.1016/j.automatica.2010.09.009. Google Scholar

show all references

References:

[1]	P. Bolzern, P. Colaneri and G. De Nicolao, Stochastic stability of positive Markov jump linear systems, Automatica, 50 (2014), 1181-1187. doi: 10.1016/j.automatica.2014.02.016. Google Scholar
[2]	X. H. Chang and G. H. Yang, New results on output feedback $H_\infty$ control for linear discrete-time systems, IEEE Transactions on Automatic Control, 59 (2014), 1355-1359. doi: 10.1109/TAC.2013.2289706. Google Scholar
[3]	J. Cheng, J. H. Park, L. Zhang and Y. Zhu, An asynchronous operation approach to event-triggered control for fuzzy Markovian jump systems with general switching policies, IEEE Transactions on Fuzzy Systems, 26 (2018), 6-18. doi: 10.1109/TFUZZ.2016.2633325. Google Scholar
[4]	D. V. Dimarogonas, E. Frazzoli and K. H. Johansson, Distributed event-triggered control for multi-agent systems, IEEE Transactions on Automatic Control, 57 (2012), 1291-1297. doi: 10.1109/TAC.2011.2174666. Google Scholar
[5]	H. Dong, Z. Wang, D. W. C. Ho and H. Gao, Robust $ H_{\infty} $ Filtering for Markovian Jump Systems With Randomly Occurring Nonlinearities and Sensor Saturation: The Finite-Horizon Case, IEEE Transactions on Signal Processing, 59 (2011), 3048-3057. doi: 10.1109/TSP.2011.2135854. Google Scholar
[6]	Y. Dong, E. Tian and Q. L. Han, A delay system method for designing event-triggered controllers of networked control systems, IEEE Transactions on Automatic Control, 58 (2013), 475-481. doi: 10.1109/TAC.2012.2206694. Google Scholar
[7]	S. He, Non-fragile passive controller design for nonlinear Markovian jumping systems via observer-based controls, Neurocomputing, 147 (2015), 350-357. doi: 10.1016/j.neucom.2014.06.053. Google Scholar
[8]	W. P. M. H. Heemels, M. C. F. Donkers and A. R. Teel, Periodic event-triggered control for linear systems, IEEE Transactions on Automatic Control, 58 (2013), 847-861. doi: 10.1109/TAC.2012.2220443. Google Scholar
[9]	F. Li, P. Lim, C. C. Shi and L. Wu, Fault detection filtering for nonhomogeneous Markovian jump systems via fuzzy approach, IEEE Transactions on Fuzzy Systems, 26 (2018), 131-141. doi: 10.1109/TFUZZ.2016.2641022. Google Scholar
[10]	H. Li, Z. Chen, L. Wu, H. K. Lam and H Du, Event-triggered fault detection of nonlinear networked systems, IEEE Transactions on Cybernetics, 47 (2017), 1041-1052. doi: 10.1109/TCYB.2016.2536750. Google Scholar
[11]	H. Li, Y. Wang, D. Yao and R. Lu, A sliding mode approach to stabilization of nonlinear Markovian jump singularly perturbed systems, Automatic, 97 (2018), 404-413. doi: 10.1016/j.automatica.2018.03.066. Google Scholar
[12]	H. Liang, L. Zhang, H. R. Karimi and Q. Zhou, Fault estimation for a class of nonlinear sem-Markovian jump systems with partly unknown transition rates and output quantization, International Journal of Robust and Nonlinear Control, 28 (2018), 5962-5980. doi: 10.1002/rnc.4353. Google Scholar
[13]	M. Liu, D. W. C. Ho and P. Shi, Adaptive fault-tolerant compensation control for Markovian jump systems with mismatched external disturbance, Automatic, 58 (2015), 5-14. doi: 10.1016/j.automatica.2015.04.022. Google Scholar
[14]	Y. Liu, Y. Yin, K. L. Teo, S. Wang and F. Liu, Probabilistic control of Markov jump systems by scenario optimization approach, Journal of Industrial and Management Optimization, 15 (2019), 1447-1453. doi: 10.3934/jimo.2018103. Google Scholar
[15]	S. Ma and E. K. Boukas, A singular system approach to robust sliding mode control for uncertain Markov jump systems, Automatica, 45 (2009), 2707-2713. doi: 10.1016/j.automatica.2009.07.027. Google Scholar
[16]	M. Mariton, Jump Linear Systems in Automatic Control, New York: M. Dekker, 1990. Google Scholar
[17]	N. Meskin and K. Khorasani, Fault detection and isolation of discrete-time Markovian jump linear systems with application to a network of multi-agent systems having imperfect communication channels, Automatic, 45 (2009), 2032-2040. doi: 10.1016/j.automatica.2009.04.020. Google Scholar
[18]	C. Peng and T. C. Yang, Event-triggered communication and ${H_\infty }$ control co-design for networked control systems, Automatic, 49 (2013), 1326-1332. doi: 10.1016/j.automatica.2013.01.038. Google Scholar
[19]	P. Shi, Y. Zhang, M. Chadli and R. X. Agarwal, Mixed H-infinity and passive filtering for discrete fuzzy neural networks with stochastic jumps and time delays, IEEE Transactions on Neural Networks and Learning Systems, 27 (2016), 903-909. doi: 10.1109/TNNLS.2015.2425962. Google Scholar
[20]	Z. Wang, Y. Liu and X. Liu, Exponential stabilization of a class of stochastic system with Markovian jump parameters and mode-dependent mixed time-delays, IEEE Transactions on Automatic Control, 55 (2010), 1656-1662. doi: 10.1109/TAC.2010.2046114. Google Scholar
[21]	L. Wu, P. Shi, H. Gao and C. Wang, ${H_\infty }$ filtering for 2D Markovian jump systems, Automatic, 44 (2008), 1849-1858. doi: 10.1016/j.automatica.2007.10.027. Google Scholar
[22]	L. Wu, X. Yao and W. X. Zheng, Generalized ${H_2 }$ fault detection for two-dimensional Markovian jump systems, Automatic, 48 (2012), 1741-1750. doi: 10.1016/j.automatica.2012.05.024. Google Scholar
[23]	Z. G. Wu, P. Shi, Z. Shu, H. Su and R. Lu, Passivity-based asynchronous control for Markov jump systems, IEEE Transactions on Automatic Control, 62 (2017), 2020-2025. doi: 10.1109/TAC.2016.2593742. Google Scholar
[24]	S. Xu, T. Chen and J. Lam, Robust ${H_\infty }$ filtering for uncertain Markovian jump systems with mode-dependent time delays, IEEE Transactions on Automatic Control, 48 (2003), 900-907. doi: 10.1109/TAC.2003.811277. Google Scholar
[25]	Y. Yin and Z. Lin, Constrained control of uncertain nonhomogeneous Markovian jump systems, International Journal of Robust and Nonlinear Control, 27 (2017), 3937-3950. Google Scholar
[26]	Y. Yin, Y. Liu, K. L. Teo and S. Wang, Event-triggered probabilistic robust control of linear systems with input constrains: By scenario optimization approach, International Journal of Robust and Nonlinear Control, 28 (2018), 144-153. doi: 10.1002/rnc.3858. Google Scholar
[27]	S. Yu, T. Qu, F. Xu, H. Chen and Y. Hu, Stability of finite horizon model predictive control with incremental input constraints, Automatic, 79 (2017), 265-272. doi: 10.1016/j.automatica.2017.01.040. Google Scholar
[28]	H. Zhang, Y. Shi and J. Wang, On energy-to-peak filtering for nonuniformly sampled nonlinear systems: A Markovian jump system approach, IEEE Transactions on Fuzzy Systems, 22 (2014), 212-222. doi: 10.1109/TFUZZ.2013.2250291. Google Scholar
[29]	X. Zhao, X. Zheng, D. Yao and L. Wu, Adaptive tracking control for a class of uncertain switched nonlinear systems, Automatica, 52 (2015), 185-191. doi: 10.1016/j.automatica.2014.11.019. Google Scholar
[30]	H. Zhang, G. Zhang and J. Wang, $H_\infty$ observer design for LPV systems with uncertain measurements on scheduling variables: application to an electric ground vehicle, IEEE/ASME Transactions on Mechatronics, 21 (2016), 1659-1670. doi: 10.1109/TMECH.2016.2522759. Google Scholar
[31]	H. Zhang and J. Wang, Active steering actuator fault detection for an automatically-steered electric ground vehicle, IEEE Transactions on Vehicular Technology, 66 (2016), 3685-3702. doi: 10.1109/TVT.2016.2604759. Google Scholar
[32]	M. Zhang, P. Shi, L. Ma, J. Cai and H. Su, Network-based fuzzy control for nonlinear Markov jump systems subject to quantization and dropout compensation, Fuzzy Sets and Systems, 371 (2019), 96-109. doi: 10.1016/j.fss.2018.09.007. Google Scholar
[33]	L. Zhang, ${H_\infty }$ estimation for discrete-time piecewise homogeneous Markov jump linear systems, Automatic, 45 (2009), 2570-2576. doi: 10.1016/j.automatica.2009.07.004. Google Scholar
[34]	X. M. Zhang and Q. L. Han, Event-based ${H_\infty }$ filtering for sampled-data systems, Automatica, 51 (2015), 55-69. doi: 10.1016/j.automatica.2014.10.092. Google Scholar
[35]	Y. Zhang, Y. He, M. Wu and J. Zhang, Stabilization for Markovian jump systems with partial information on transition probability based on free-connection weighting matrices, Automatica, 47 (2011), 79-84. doi: 10.1016/j.automatica.2010.09.009. Google Scholar

Figure 1. System mode trajectory

Figure Options

Download full-size image

Download as PowerPoint slide

Figure 2. System states curve

Figure Options

Download full-size image

Download as PowerPoint slide

Figure 3. Triggered instants diagram

Figure Options

Download full-size image

Download as PowerPoint slide

Figure 4. Control curve

Figure Options

Download full-size image

Download as PowerPoint slide

Figure 5. System mode trajectory

Figure Options

Download full-size image

Download as PowerPoint slide

Figure 6. System states curve

Figure Options

Download full-size image

Download as PowerPoint slide

Figure 7. Triggered instants diagram

Figure Options

Download full-size image

Download as PowerPoint slide

Figure 8. Control curve

Figure Options

Download full-size image

Download as PowerPoint slide

[1]	Hui Lv, Xing'an Wang. Dissipative control for uncertain singular markovian jump systems via hybrid impulsive control. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 127-142. doi: 10.3934/naco.2020020
[2]	Max E. Gilmore, Chris Guiver, Hartmut Logemann. Sampled-data integral control of multivariable linear infinite-dimensional systems with input nonlinearities. Mathematical Control & Related Fields, 2021 doi: 10.3934/mcrf.2021001
[3]	Manuel de León, Víctor M. Jiménez, Manuel Lainz. Contact Hamiltonian and Lagrangian systems with nonholonomic constraints. Journal of Geometric Mechanics, 2020 doi: 10.3934/jgm.2021001
[4]	Zsolt Saffer, Miklós Telek, Gábor Horváth. Analysis of Markov-modulated fluid polling systems with gated discipline. Journal of Industrial & Management Optimization, 2021, 17 (2) : 575-599. doi: 10.3934/jimo.2019124
[5]	Stefan Doboszczak, Manil T. Mohan, Sivaguru S. Sritharan. Pontryagin maximum principle for the optimal control of linearized compressible navier-stokes equations with state constraints. Evolution Equations & Control Theory, 2020 doi: 10.3934/eect.2020110
[6]	Awais Younus, Zoubia Dastgeer, Nudrat Ishaq, Abdul Ghaffar, Kottakkaran Sooppy Nisar, Devendra Kumar. On the observability of conformable linear time-invariant control systems. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020444
[7]	Duy Phan, Lassi Paunonen. Finite-dimensional controllers for robust regulation of boundary control systems. Mathematical Control & Related Fields, 2021, 11 (1) : 95-117. doi: 10.3934/mcrf.2020029
[8]	Angelica Pachon, Federico Polito, Costantino Ricciuti. On discrete-time semi-Markov processes. Discrete & Continuous Dynamical Systems - B, 2021, 26 (3) : 1499-1529. doi: 10.3934/dcdsb.2020170
[9]	Xuefeng Zhang, Yingbo Zhang. Fault-tolerant control against actuator failures for uncertain singular fractional order systems. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 1-12. doi: 10.3934/naco.2020011
[10]	Pierluigi Colli, Gianni Gilardi, Jürgen Sprekels. Deep quench approximation and optimal control of general Cahn–Hilliard systems with fractional operators and double obstacle potentials. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 243-271. doi: 10.3934/dcdss.2020213
[11]	Simone Fiori. Error-based control systems on Riemannian state manifolds: Properties of the principal pushforward map associated to parallel transport. Mathematical Control & Related Fields, 2021, 11 (1) : 143-167. doi: 10.3934/mcrf.2020031
[12]	Biao Zeng. Existence results for fractional impulsive delay feedback control systems with Caputo fractional derivatives. Evolution Equations & Control Theory, 2021 doi: 10.3934/eect.2021001
[13]	Puneet Pasricha, Anubha Goel. Pricing power exchange options with hawkes jump diffusion processes. Journal of Industrial & Management Optimization, 2021, 17 (1) : 133-149. doi: 10.3934/jimo.2019103
[14]	Joel Kübler, Tobias Weth. Spectral asymptotics of radial solutions and nonradial bifurcation for the Hénon equation. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3629-3656. doi: 10.3934/dcds.2020032
[15]	Xuemei Chen, Julia Dobrosotskaya. Inpainting via sparse recovery with directional constraints. Mathematical Foundations of Computing, 2020, 3 (4) : 229-247. doi: 10.3934/mfc.2020025
[16]	Junkee Jeon. Finite horizon portfolio selection problems with stochastic borrowing constraints. Journal of Industrial & Management Optimization, 2021, 17 (2) : 733-763. doi: 10.3934/jimo.2019132
[17]	Nan Zhang, Linyi Qian, Zhuo Jin, Wei Wang. Optimal stop-loss reinsurance with joint utility constraints. Journal of Industrial & Management Optimization, 2021, 17 (2) : 841-868. doi: 10.3934/jimo.2020001
[18]	Wei Ouyang, Li Li. Hölder strong metric subregularity and its applications to convergence analysis of inexact Newton methods. Journal of Industrial & Management Optimization, 2021, 17 (1) : 169-184. doi: 10.3934/jimo.2019105
[19]	Aihua Fan, Jörg Schmeling, Weixiao Shen. $ L^\infty $-estimation of generalized Thue-Morse trigonometric polynomials and ergodic maximization. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 297-327. doi: 10.3934/dcds.2020363
[20]	Xin Zhao, Tao Feng, Liang Wang, Zhipeng Qiu. Threshold dynamics and sensitivity analysis of a stochastic semi-Markov switched SIRS epidemic model with nonlinear incidence and vaccination. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2021010

2019 Impact Factor: 1.366

Tools

Metrics

Tools

Article outline

Figures and Tables

2019 Impact Factor: 1.366

Tools

Figures and Tables

2019 Impact Factor: 1.366

American Institute of Mathematical Sciences

Event-triggered mixed $ H_\infty $ and passive control for Markov jump systems with bounded inputs

References:

References:

Tools

Metrics

Other articles
by authors

Tools

Tools

Tools

Metrics

Other articles
by authors

American Institute of Mathematical Sciences

Event-triggered mixed $ H_\infty $ and passive control for Markov jump systems with bounded inputs

References:

References:

Tools

Metrics

Other articlesby authors

Tools

Tools

Tools

Metrics

Other articlesby authors

Other articles
by authors

Other articles
by authors