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Necessary and sufficient conditions for stability of impulsive switched linear systems
Stabilization of discrete-time Markovian jump systems with partially unknown transition probabilities
1. | Institute of Systems Science, Northeastern University, Shenyang, Liaoning, 110819, China, China |
2. | School of Information and Control Engineering, Liaoning Shihua University, Fushun, Liaoning 113001, China |
3. | Department of Computing, Curtin University of Technology, Perth, WA 6102, Australia |
References:
[1] |
E. Boukas and Z. Liu, Robust $H_\infty$ control of discrete-time Markovian jump linear systems with mode-dependent time-delays, IEEE Transactions on Automatic Control, 46 (2001), 1918-1924. |
[2] |
W. Chen, Z. Guan and P. Yu, Delay-dependent stability and $H_\infty$ control of uncertain discrete-time Markovian jump systems with mode-dependent time delays, Systems and Control Letters, 52 (2004), 361-376. |
[3] |
O. Costa, Stability results for discrete-time linear systems with Markovian jumping parameters, Journal of Mathematical Analysis and Applications, 179 (1993), 154-178.
doi: 10.1006/jmaa.1993.1341. |
[4] |
C. de Souza, Robust stability and stabilization of uncertain discrete-time Markovian jump linear systems, IEEE Transactions on Automatic Control, 51 (2006), 836-841.
doi: 10.1109/TAC.2006.875012. |
[5] |
Y. Dong and J. Sun, On hybrid control of a class of stochastic non-linear Markovian switching systems, Automatica, 44 (2008), 990-995.
doi: 10.1016/j.automatica.2007.08.006. |
[6] |
L. Ghaoui, F. Oustry and M. AitRami, A cone complementarity linearization algorithm for static output-feedback and related problems, IEEE Transactions on Automatic Control, 42 (1997), 1171-1176.
doi: 10.1109/9.618250. |
[7] |
Z. Guan, D. Hill and X. Shen, On hybrid impulsive and switching systems and application to nonlinear control, IEEE Transactions on Automatic Control, 50 (2005), 1058-1062.
doi: 10.1109/TAC.2005.851462. |
[8] |
P. V. Laxmi and O. M. Yesuf, Analysis of a finite buffer general input queue with Markovian service process and accessible and non-accessible batch service, Journal of Industrial and Management Optimization, 6 (2010), 929-944.
doi: 10.3934/jimo.2010.6.929. |
[9] |
F. Leibfritz, An LMI-based algorithm for designing suboptimal static $H_2$/$H_\infty$ output feedback controllers, SIAM Journal on Control and Optimization, 39 (2001), 1171-1735. |
[10] |
S. Pan, J. Sun and S. Zhao, Stabilization of discrete-time Markovian jump linear systems via time-delayed and impulsive controllers, Automatica, 44 (2008), 2954-2958.
doi: 10.1016/j.automatica.2008.04.004. |
[11] |
P. Seiler and R. Sengupta, A bounded real lemma for jump systems, IEEE Transactions on Automatic Control, 48 (2003), 1651-1654.
doi: 10.1109/TAC.2003.817010. |
[12] |
P. Shi, E. Boukas and R. Agarwal, Control of Markovian jump discrete-time systems with norm bounded uncertainty and unknown delay, IEEE Transactions on Automatic Control, 44 (1999), 2139-2144.
doi: 10.1109/9.802932. |
[13] |
P. Shi, E. Boukas and R. Agarwal, Kalman filtering for continuous-time uncertain systems with Markovian jumping parameters, IEEE Transactions on Automatic Control, 44 (1999), 1592-1597.
doi: 10.1109/9.780431. |
[14] |
Y. Shi, P. Shi and M. S. Mahmoud, $H_\infty$ and robust control of interconnected systems with Markovian jump parameters, Discrete and Continuous Dynamical Systems-Series B, 5 (2005), 365-384. |
[15] |
M. Telek and Z. Saffer, Analysis of globally gated Markovian limited cyclic polling model and its application to uplink traffic in the IEEE 802.16 network, Journal of Industrial and Management Optimization, 7 (2011), 677-697.
doi: 10.3934/jimo.2011.7.677. |
[16] |
G. Wang, Q. Zhang and V. Sreeram, Robust delay-range-dependent stabilization for Markovian jump systems with mode-dependent time delays and nonlinearities, Optimal Control Applications and Methods, 31 (2010), 249-264. |
[17] |
G. Wang, Q. Zhang and V. Sreeram, $H_\infty$ control for discrete-time singularly perturbed systems with two Markov processes, Journal of The Franklin Institute, 347 (2010), 836-847.
doi: 10.1016/j.jfranklin.2010.03.007. |
[18] |
H. Wu and J. Sun, $p$-Moment stability of stochastic differential equations with impulsvie jump and Markovian switching, Automatica, 42 (2006), 1753-1759.
doi: 10.1016/j.automatica.2006.05.009. |
[19] |
J. Xiong, J. Lam, H. Gao and D. Ho, On robust stabilization of Markovian jump systems with uncertain switching probabilities, Automatica, 41 (2005), 897-903.
doi: 10.1016/j.automatica.2004.12.001. |
[20] |
J. Xiong and J. Lam, Stabilization of discrete-time Markovian jump linear systems via time-delyed controllers, Automatica, 42 (2006), 747-753.
doi: 10.1016/j.automatica.2005.12.015. |
[21] |
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. |
[22] |
S. Xu and J. Lam, Delay-dependent $H_\infty$ control and filtering for uncertain Markovian jump systems with time-varying delays, IEEE Transactions on Circuits and Systems, 54 (2007), 2070-2077.
doi: 10.1109/TCSI.2007.904640. |
[23] |
Z. Yang and D. Xu, Stability analysis and design of impulsive control systems with time delay, IEEE Transactions on Automatic Control, 52 (2007), 1448-1454.
doi: 10.1109/TAC.2007.902748. |
[24] |
L. Zhang and E. Boukas, Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities, Automatica, 45 (2009), 463-468.
doi: 10.1016/j.automatica.2008.08.010. |
[25] |
L. Zhang and E. Boukas, $H_\infty$ control for discrete-time Markovian jump linear systems with partly unknown transition probabilities, International Journal of Robust and Nonlinear Control, 19 (2009), 868-883.
doi: 10.1002/rnc.1355. |
show all references
References:
[1] |
E. Boukas and Z. Liu, Robust $H_\infty$ control of discrete-time Markovian jump linear systems with mode-dependent time-delays, IEEE Transactions on Automatic Control, 46 (2001), 1918-1924. |
[2] |
W. Chen, Z. Guan and P. Yu, Delay-dependent stability and $H_\infty$ control of uncertain discrete-time Markovian jump systems with mode-dependent time delays, Systems and Control Letters, 52 (2004), 361-376. |
[3] |
O. Costa, Stability results for discrete-time linear systems with Markovian jumping parameters, Journal of Mathematical Analysis and Applications, 179 (1993), 154-178.
doi: 10.1006/jmaa.1993.1341. |
[4] |
C. de Souza, Robust stability and stabilization of uncertain discrete-time Markovian jump linear systems, IEEE Transactions on Automatic Control, 51 (2006), 836-841.
doi: 10.1109/TAC.2006.875012. |
[5] |
Y. Dong and J. Sun, On hybrid control of a class of stochastic non-linear Markovian switching systems, Automatica, 44 (2008), 990-995.
doi: 10.1016/j.automatica.2007.08.006. |
[6] |
L. Ghaoui, F. Oustry and M. AitRami, A cone complementarity linearization algorithm for static output-feedback and related problems, IEEE Transactions on Automatic Control, 42 (1997), 1171-1176.
doi: 10.1109/9.618250. |
[7] |
Z. Guan, D. Hill and X. Shen, On hybrid impulsive and switching systems and application to nonlinear control, IEEE Transactions on Automatic Control, 50 (2005), 1058-1062.
doi: 10.1109/TAC.2005.851462. |
[8] |
P. V. Laxmi and O. M. Yesuf, Analysis of a finite buffer general input queue with Markovian service process and accessible and non-accessible batch service, Journal of Industrial and Management Optimization, 6 (2010), 929-944.
doi: 10.3934/jimo.2010.6.929. |
[9] |
F. Leibfritz, An LMI-based algorithm for designing suboptimal static $H_2$/$H_\infty$ output feedback controllers, SIAM Journal on Control and Optimization, 39 (2001), 1171-1735. |
[10] |
S. Pan, J. Sun and S. Zhao, Stabilization of discrete-time Markovian jump linear systems via time-delayed and impulsive controllers, Automatica, 44 (2008), 2954-2958.
doi: 10.1016/j.automatica.2008.04.004. |
[11] |
P. Seiler and R. Sengupta, A bounded real lemma for jump systems, IEEE Transactions on Automatic Control, 48 (2003), 1651-1654.
doi: 10.1109/TAC.2003.817010. |
[12] |
P. Shi, E. Boukas and R. Agarwal, Control of Markovian jump discrete-time systems with norm bounded uncertainty and unknown delay, IEEE Transactions on Automatic Control, 44 (1999), 2139-2144.
doi: 10.1109/9.802932. |
[13] |
P. Shi, E. Boukas and R. Agarwal, Kalman filtering for continuous-time uncertain systems with Markovian jumping parameters, IEEE Transactions on Automatic Control, 44 (1999), 1592-1597.
doi: 10.1109/9.780431. |
[14] |
Y. Shi, P. Shi and M. S. Mahmoud, $H_\infty$ and robust control of interconnected systems with Markovian jump parameters, Discrete and Continuous Dynamical Systems-Series B, 5 (2005), 365-384. |
[15] |
M. Telek and Z. Saffer, Analysis of globally gated Markovian limited cyclic polling model and its application to uplink traffic in the IEEE 802.16 network, Journal of Industrial and Management Optimization, 7 (2011), 677-697.
doi: 10.3934/jimo.2011.7.677. |
[16] |
G. Wang, Q. Zhang and V. Sreeram, Robust delay-range-dependent stabilization for Markovian jump systems with mode-dependent time delays and nonlinearities, Optimal Control Applications and Methods, 31 (2010), 249-264. |
[17] |
G. Wang, Q. Zhang and V. Sreeram, $H_\infty$ control for discrete-time singularly perturbed systems with two Markov processes, Journal of The Franklin Institute, 347 (2010), 836-847.
doi: 10.1016/j.jfranklin.2010.03.007. |
[18] |
H. Wu and J. Sun, $p$-Moment stability of stochastic differential equations with impulsvie jump and Markovian switching, Automatica, 42 (2006), 1753-1759.
doi: 10.1016/j.automatica.2006.05.009. |
[19] |
J. Xiong, J. Lam, H. Gao and D. Ho, On robust stabilization of Markovian jump systems with uncertain switching probabilities, Automatica, 41 (2005), 897-903.
doi: 10.1016/j.automatica.2004.12.001. |
[20] |
J. Xiong and J. Lam, Stabilization of discrete-time Markovian jump linear systems via time-delyed controllers, Automatica, 42 (2006), 747-753.
doi: 10.1016/j.automatica.2005.12.015. |
[21] |
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. |
[22] |
S. Xu and J. Lam, Delay-dependent $H_\infty$ control and filtering for uncertain Markovian jump systems with time-varying delays, IEEE Transactions on Circuits and Systems, 54 (2007), 2070-2077.
doi: 10.1109/TCSI.2007.904640. |
[23] |
Z. Yang and D. Xu, Stability analysis and design of impulsive control systems with time delay, IEEE Transactions on Automatic Control, 52 (2007), 1448-1454.
doi: 10.1109/TAC.2007.902748. |
[24] |
L. Zhang and E. Boukas, Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities, Automatica, 45 (2009), 463-468.
doi: 10.1016/j.automatica.2008.08.010. |
[25] |
L. Zhang and E. Boukas, $H_\infty$ control for discrete-time Markovian jump linear systems with partly unknown transition probabilities, International Journal of Robust and Nonlinear Control, 19 (2009), 868-883.
doi: 10.1002/rnc.1355. |
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