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Piecewise observers of rectangular discrete fuzzy descriptor systems with multiple time-varying delays
1. | School of Mathematics Sicences, Dezhou University, Dezhou 253600, China |
2. | School of Mathematics, Shandong University, Jinan 250100, China, China |
References:
[1] |
S. Boyd, L. Ghaoui, E. Feron and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory,, Society for Industrial and Applied Mathematics, (1994).
doi: 10.1137/1.9781611970777.fm. |
[2] |
S. Cao, N. W. Rees and G. Feng, Analysis and design of fuzzy control systems using dynamic fuzzy-state space models,, IEEE Transactions on Fuzzy Systems, 7 (1999), 192.
doi: 10.1109/91.755400. |
[3] |
Y. Y. Cao and P. M. Frank, Robust $H_{\infty}$ disturbance attenuation for a class of uncertain discrete-time fuzzy systems,, IEEE Transactions on Fuzzy Systems, 8 (2000), 406.
doi: 10.1109/91.868947. |
[4] |
Q. Chai, L. Ryan, K. Teo and C. Yang, A unified parameter identification method for nonlinear time-delay systems,, Journal of Industrial and Management Optimization, 9 (2013), 471.
doi: 10.3934/jimo.2013.9.471. |
[5] |
B. S. Chen, C. H. Tseng and H. J. Uang, Mixed $H_{2}/H_{\infty}$ fuzzy output feedback control design for nonlinear dynamic systems: An LMI approach,, IEEE Transactions on Fuzzy Systems, 8 (2000), 249.
doi: 10.1109/91.855915. |
[6] |
M. Darouach, M. Zasadzinski and M. Hayar, Reduced-order observer design for descriptor systems with unknown inputs,, IEEE Transactions on Automatic Control, 41 (1996), 1068.
doi: 10.1109/9.508918. |
[7] |
D. Essawy, Adaptive control of nonlinear systems using fuzzy systems,, Journal of Industrial and Management Optimization, 6 (2010), 861.
doi: 10.3934/jimo.2010.6.861. |
[8] |
G. Feng, Stability analysis of discrete-time fuzzy dynamic systems based on piecewise Lyapunov functions,, IEEE Transactions on Fuzzy Systems, 12 (2004), 22.
doi: 10.1109/TFUZZ.2003.819833. |
[9] |
H. Gao and T. Chen, New results on stability of discrete-time systems with time-varying state delay,, IEEE Transactions on Automatic Control, 52 (2007), 328.
doi: 10.1109/TAC.2006.890320. |
[10] |
H. Gao, J. Lam, C. Wang and Y. Wang, Delay-dependent output-feedback stabilisation of discrete-time systems with time-varying state delay,, IEE Proceedings-Control Theory and Applications, 151 (2004), 691.
doi: 10.1049/ip-cta:20040822. |
[11] |
Z. Gao, X. Shi and S. Ding, Fuzzy state/disturbance observer design for T-S fuzzy systems with application to sensor fault estimation,, IEEE Transactions on Systems, 38 (2008), 875.
doi: 10.1109/TSMCB.2008.917185. |
[12] |
T. M. Guerra and L. Vermeiren, LMI-based relaxed nonquadratic stabilization conditions for nonlinear systems in the Takagi-Sugeno's form,, Automatica, 40 (2004), 823.
doi: 10.1016/j.automatica.2003.12.014. |
[13] |
A. Hmamed, Constrained regulation of linear discrete-time systems with time delay: Delay-dependent and delay-independent conditions,, International Journal of Systems Science, 31 (2000), 529.
doi: 10.1080/002077200291109. |
[14] |
Y. Hosoe and T. Hagiwara, Robust stability analysis based on finite impulse response scaling for discrete-time linear time-invariant systems,, IET Control Theory and Applications, 7 (2013), 1463.
doi: 10.1049/iet-cta.2013.0053. |
[15] |
C. Jiang, K. Teo, R. Loxton and G. Duan, A neighboring extremal solution for an optimal switched impulsive control problem,, Journal of Industrial and Management Optimization, 8 (2012), 591.
doi: 10.3934/jimo.2012.8.591. |
[16] |
M. Johansson, A. Rantzer and K.-E. Årzén, Piecewise quadratic stability of fuzzy systems,, IEEE Transactions on Fuzzy Systems, 7 (1999), 713.
doi: 10.1109/91.811241. |
[17] |
D. Koenig, Unknown input proportional multiple-integral observer design for linear descriptor systems: application to state and fault estimation,, IEEE Transactions on Automatic Control, 50 (2005), 212.
doi: 10.1109/TAC.2004.841889. |
[18] |
A. Kumar and P. Daoutidis, Control of Nonlinear Differential Algebraic Equation Systems with Applications to Chemical Processes,, Chapman & Hall/CRC, (1999).
doi: 10.1007/978-94-017-3594-0_4. |
[19] |
F. Li, P. Shi, L. Wu and X. Zhang, Fuzzy-model-based D-stability and non-fragile control for discrete-time descriptor systems with multiple delays,, IEEE Transactions on Fuzzy Systems, 22 (2013), 1019.
doi: 10.1109/TFUZZ.2013.2272647. |
[20] |
X. Liu and Q. Zhang, New approaches to $H_{\infty}$ controller designs based on fuzzy observers for T-S fuzzy systems via LMI,, Automatica, 39 (2003), 1571.
doi: 10.1016/S0005-1098(03)00172-9. |
[21] |
S. Ma and Z. Cheng, Observer design for discrete time-delay singular systems with unknown inputs,, American Control Conference, 6 (2005), 4215.
doi: 10.1109/ACC.2005.1470640. |
[22] |
Y. Ma and G. Yang, Stability analysis for linear discrete-time systems subject to actuator saturation,, Control Theory and Technology, 8 (2010), 245.
doi: 10.1007/s11768-010-7261-9. |
[23] |
S. K. Nguang and P. Shi, $H_{\infty}$ fuzzy output feedback control design for nonlinear systems: An LMI approach,, IEEE Transactions on Fuzzy Systems, 11 (2003), 331.
doi: 10.1109/TFUZZ.2003.812691. |
[24] |
R. Palm and P. Bergsten, Sliding mode observer for a Takagi-Sugeno fuzzy system,, The Ninth IEEE International Conference on Fuzzy Systems, 2 (2000), 665.
doi: 10.1109/FUZZY.2000.839072. |
[25] |
J. Qiu, G. Feng and H. Gao, Static-Output-Feedback control of continuous-time T-S fuzzy affine systems via piecewise Lyapunov functions,, IEEE Transactions on Fuzzy Systems, 21 (2013), 245.
doi: 10.1109/TFUZZ.2012.2210555. |
[26] |
J. Qiu, G. Feng and H. Gao, Observer-based piecewise affine output feedback controller synthesis of continuous-time T-S fuzzy affine dynamic systems using quantized measurements,, IEEE Transactions on Fuzzy Systems, 20 (2012), 1046.
doi: 10.1109/TFUZZ.2012.2191790. |
[27] |
J. Qiu, G. Feng and H. Gao, Fuzzy-model-based piecewise $H_{\infty}$ static-output-feedback controller design for networked nonlinear systems,, IEEE Transactions on Fuzzy Systems, 18 (2010), 919.
doi: 10.1109/TFUZZ.2010.2052259. |
[28] |
R. Riaza, Differential-Algebraic Systems: Analytical Aspects And Circuit Applications,, World Scientific, (2008).
doi: 10.1016/0098-1354(88)85052-X. |
[29] |
H. Shi, G. Xie and W. Luo, Controllability analysis of linear discrete time systems with time delay in state,, Abstract and Applied Analysis, (2012).
doi: 10.1155/2012/490903. |
[30] |
T. Takagi and M. Sugeno, Fuzzy identification of systems and its applications to modeling and control,, IEEE Transactions on Systems, 15 (1985), 116. Google Scholar |
[31] |
T. Taniguchi, K. Tanaka, K. Yamafuji and H. Wang, Fuzzy descriptor systems:stability analysis and design via LMIs,, American Control Conference, 3 (1999), 1827.
doi: 10.1109/ACC.1999.786165. |
[32] |
Y. C. Wang, J. S. Wang and F. H. Tsai, Analysis of discrete-time space priority queue with fuzzy threshold,, Journal of Industrial and Management Optimization, 5 (2009), 467.
doi: 10.3934/jimo.2009.5.467. |
[33] |
Z. Wang, Y. Shen, X. Zhang and Q. Wang, Observer design for discrete-time descriptor systems: An LMI approach,, Systems & Control Letters, 61 (2012), 683.
doi: 10.1016/j.sysconle.2012.03.006. |
[34] |
J. Xiong and J. Lam, Stabilization of linear systems over networks with bounded packet loss,, Automatica, 43 (2007), 80.
doi: 10.1016/j.automatica.2006.07.017. |
[35] |
S. Xu and J. Lam, Robust $H_{\infty}$ control for uncertain discrete-time-delay fuzzy systems via output feedback controllers,, IEEE Transactions on Fuzzy Systems, 13 (2005), 82.
doi: 10.1109/TFUZZ.2004.839661. |
[36] |
Q. Zhang, C. Liu and X. Zhang, Complexity, Analysis and Control of Singular Biological Systems,, Springer, (2012).
doi: 10.1007/978-1-4471-2303-3. |
[37] |
B. Zhu, Q. Zhang and C. Chang, Delay-dependent disspative control for a class of non-linear system via Takagi-Sugeno fuzzy descriptor model with time delay,, IET Control Theory and Applications, 8 (2014), 451.
doi: 10.1049/iet-cta.2013.0438. |
show all references
References:
[1] |
S. Boyd, L. Ghaoui, E. Feron and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory,, Society for Industrial and Applied Mathematics, (1994).
doi: 10.1137/1.9781611970777.fm. |
[2] |
S. Cao, N. W. Rees and G. Feng, Analysis and design of fuzzy control systems using dynamic fuzzy-state space models,, IEEE Transactions on Fuzzy Systems, 7 (1999), 192.
doi: 10.1109/91.755400. |
[3] |
Y. Y. Cao and P. M. Frank, Robust $H_{\infty}$ disturbance attenuation for a class of uncertain discrete-time fuzzy systems,, IEEE Transactions on Fuzzy Systems, 8 (2000), 406.
doi: 10.1109/91.868947. |
[4] |
Q. Chai, L. Ryan, K. Teo and C. Yang, A unified parameter identification method for nonlinear time-delay systems,, Journal of Industrial and Management Optimization, 9 (2013), 471.
doi: 10.3934/jimo.2013.9.471. |
[5] |
B. S. Chen, C. H. Tseng and H. J. Uang, Mixed $H_{2}/H_{\infty}$ fuzzy output feedback control design for nonlinear dynamic systems: An LMI approach,, IEEE Transactions on Fuzzy Systems, 8 (2000), 249.
doi: 10.1109/91.855915. |
[6] |
M. Darouach, M. Zasadzinski and M. Hayar, Reduced-order observer design for descriptor systems with unknown inputs,, IEEE Transactions on Automatic Control, 41 (1996), 1068.
doi: 10.1109/9.508918. |
[7] |
D. Essawy, Adaptive control of nonlinear systems using fuzzy systems,, Journal of Industrial and Management Optimization, 6 (2010), 861.
doi: 10.3934/jimo.2010.6.861. |
[8] |
G. Feng, Stability analysis of discrete-time fuzzy dynamic systems based on piecewise Lyapunov functions,, IEEE Transactions on Fuzzy Systems, 12 (2004), 22.
doi: 10.1109/TFUZZ.2003.819833. |
[9] |
H. Gao and T. Chen, New results on stability of discrete-time systems with time-varying state delay,, IEEE Transactions on Automatic Control, 52 (2007), 328.
doi: 10.1109/TAC.2006.890320. |
[10] |
H. Gao, J. Lam, C. Wang and Y. Wang, Delay-dependent output-feedback stabilisation of discrete-time systems with time-varying state delay,, IEE Proceedings-Control Theory and Applications, 151 (2004), 691.
doi: 10.1049/ip-cta:20040822. |
[11] |
Z. Gao, X. Shi and S. Ding, Fuzzy state/disturbance observer design for T-S fuzzy systems with application to sensor fault estimation,, IEEE Transactions on Systems, 38 (2008), 875.
doi: 10.1109/TSMCB.2008.917185. |
[12] |
T. M. Guerra and L. Vermeiren, LMI-based relaxed nonquadratic stabilization conditions for nonlinear systems in the Takagi-Sugeno's form,, Automatica, 40 (2004), 823.
doi: 10.1016/j.automatica.2003.12.014. |
[13] |
A. Hmamed, Constrained regulation of linear discrete-time systems with time delay: Delay-dependent and delay-independent conditions,, International Journal of Systems Science, 31 (2000), 529.
doi: 10.1080/002077200291109. |
[14] |
Y. Hosoe and T. Hagiwara, Robust stability analysis based on finite impulse response scaling for discrete-time linear time-invariant systems,, IET Control Theory and Applications, 7 (2013), 1463.
doi: 10.1049/iet-cta.2013.0053. |
[15] |
C. Jiang, K. Teo, R. Loxton and G. Duan, A neighboring extremal solution for an optimal switched impulsive control problem,, Journal of Industrial and Management Optimization, 8 (2012), 591.
doi: 10.3934/jimo.2012.8.591. |
[16] |
M. Johansson, A. Rantzer and K.-E. Årzén, Piecewise quadratic stability of fuzzy systems,, IEEE Transactions on Fuzzy Systems, 7 (1999), 713.
doi: 10.1109/91.811241. |
[17] |
D. Koenig, Unknown input proportional multiple-integral observer design for linear descriptor systems: application to state and fault estimation,, IEEE Transactions on Automatic Control, 50 (2005), 212.
doi: 10.1109/TAC.2004.841889. |
[18] |
A. Kumar and P. Daoutidis, Control of Nonlinear Differential Algebraic Equation Systems with Applications to Chemical Processes,, Chapman & Hall/CRC, (1999).
doi: 10.1007/978-94-017-3594-0_4. |
[19] |
F. Li, P. Shi, L. Wu and X. Zhang, Fuzzy-model-based D-stability and non-fragile control for discrete-time descriptor systems with multiple delays,, IEEE Transactions on Fuzzy Systems, 22 (2013), 1019.
doi: 10.1109/TFUZZ.2013.2272647. |
[20] |
X. Liu and Q. Zhang, New approaches to $H_{\infty}$ controller designs based on fuzzy observers for T-S fuzzy systems via LMI,, Automatica, 39 (2003), 1571.
doi: 10.1016/S0005-1098(03)00172-9. |
[21] |
S. Ma and Z. Cheng, Observer design for discrete time-delay singular systems with unknown inputs,, American Control Conference, 6 (2005), 4215.
doi: 10.1109/ACC.2005.1470640. |
[22] |
Y. Ma and G. Yang, Stability analysis for linear discrete-time systems subject to actuator saturation,, Control Theory and Technology, 8 (2010), 245.
doi: 10.1007/s11768-010-7261-9. |
[23] |
S. K. Nguang and P. Shi, $H_{\infty}$ fuzzy output feedback control design for nonlinear systems: An LMI approach,, IEEE Transactions on Fuzzy Systems, 11 (2003), 331.
doi: 10.1109/TFUZZ.2003.812691. |
[24] |
R. Palm and P. Bergsten, Sliding mode observer for a Takagi-Sugeno fuzzy system,, The Ninth IEEE International Conference on Fuzzy Systems, 2 (2000), 665.
doi: 10.1109/FUZZY.2000.839072. |
[25] |
J. Qiu, G. Feng and H. Gao, Static-Output-Feedback control of continuous-time T-S fuzzy affine systems via piecewise Lyapunov functions,, IEEE Transactions on Fuzzy Systems, 21 (2013), 245.
doi: 10.1109/TFUZZ.2012.2210555. |
[26] |
J. Qiu, G. Feng and H. Gao, Observer-based piecewise affine output feedback controller synthesis of continuous-time T-S fuzzy affine dynamic systems using quantized measurements,, IEEE Transactions on Fuzzy Systems, 20 (2012), 1046.
doi: 10.1109/TFUZZ.2012.2191790. |
[27] |
J. Qiu, G. Feng and H. Gao, Fuzzy-model-based piecewise $H_{\infty}$ static-output-feedback controller design for networked nonlinear systems,, IEEE Transactions on Fuzzy Systems, 18 (2010), 919.
doi: 10.1109/TFUZZ.2010.2052259. |
[28] |
R. Riaza, Differential-Algebraic Systems: Analytical Aspects And Circuit Applications,, World Scientific, (2008).
doi: 10.1016/0098-1354(88)85052-X. |
[29] |
H. Shi, G. Xie and W. Luo, Controllability analysis of linear discrete time systems with time delay in state,, Abstract and Applied Analysis, (2012).
doi: 10.1155/2012/490903. |
[30] |
T. Takagi and M. Sugeno, Fuzzy identification of systems and its applications to modeling and control,, IEEE Transactions on Systems, 15 (1985), 116. Google Scholar |
[31] |
T. Taniguchi, K. Tanaka, K. Yamafuji and H. Wang, Fuzzy descriptor systems:stability analysis and design via LMIs,, American Control Conference, 3 (1999), 1827.
doi: 10.1109/ACC.1999.786165. |
[32] |
Y. C. Wang, J. S. Wang and F. H. Tsai, Analysis of discrete-time space priority queue with fuzzy threshold,, Journal of Industrial and Management Optimization, 5 (2009), 467.
doi: 10.3934/jimo.2009.5.467. |
[33] |
Z. Wang, Y. Shen, X. Zhang and Q. Wang, Observer design for discrete-time descriptor systems: An LMI approach,, Systems & Control Letters, 61 (2012), 683.
doi: 10.1016/j.sysconle.2012.03.006. |
[34] |
J. Xiong and J. Lam, Stabilization of linear systems over networks with bounded packet loss,, Automatica, 43 (2007), 80.
doi: 10.1016/j.automatica.2006.07.017. |
[35] |
S. Xu and J. Lam, Robust $H_{\infty}$ control for uncertain discrete-time-delay fuzzy systems via output feedback controllers,, IEEE Transactions on Fuzzy Systems, 13 (2005), 82.
doi: 10.1109/TFUZZ.2004.839661. |
[36] |
Q. Zhang, C. Liu and X. Zhang, Complexity, Analysis and Control of Singular Biological Systems,, Springer, (2012).
doi: 10.1007/978-1-4471-2303-3. |
[37] |
B. Zhu, Q. Zhang and C. Chang, Delay-dependent disspative control for a class of non-linear system via Takagi-Sugeno fuzzy descriptor model with time delay,, IET Control Theory and Applications, 8 (2014), 451.
doi: 10.1049/iet-cta.2013.0438. |
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