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Event-triggered mixed $ H_\infty $ and passive control for Markov jump systems with bounded inputs
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 |
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.
References:
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Stochastic stability of positive Markov jump linear systems, Automatica, 50 (2014), 1181-1187.
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X. H. Chang and G. H. Yang,
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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.
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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.
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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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
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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.
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[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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.
|
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[16] |
M. Mariton, Jump Linear Systems in Automatic Control, New York: M. Dekker, 1990. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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.
|
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |








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