Stochastic stability of semi-Markovian jump systems with mode-dependent delays

International Journal of Robust and Nonlinear Control

Volumn 24, Issue 18, 2014, Pages 3317-3330

  Li, Fanbiao ^a   Wu, Ligang ^a   Shi, Peng ^b,c  

^a HARBIN INSTITUTE OF TECHNOLOGY   (China)

^b UNIVERSITY OF ADELAIDE   (Australia)

^c VICTORIA UNIVERSITY   (Australia)

Author keywords

Mode dependent time delays; Semi Markovian jump systems; Stochastic stability

Indexed keywords

DYNAMICAL SYSTEMS; LYAPUNOV FUNCTIONS; MARKOV PROCESSES; STOCHASTIC SYSTEMS; TIME DELAY;

ANALYSIS METHOD; LYAPUNOV FUNCTION APPROACHES; MARKOVIAN JUMP SYSTEMS; MODE-DEPENDENT TIME DELAYS; RELAXED CONDITIONS; STOCHASTIC STABILITY; TRANSITION RATES; UNDERLYING SYSTEMS;

SYSTEM STABILITY;

EID: 84911386188     PISSN: 10498923     EISSN: 10991239     Source Type: Journal    
DOI: 10.1002/rnc.3057     Document Type: Article

References (38)

1. Calafiore G, Dabbene F. Observer design with guaranteed RMS gain for discrete-time LPV systems with Markovian jumps. International Journal of Robust and Nonlinear Control 2009; 19(6):676-691.
2. ∞ filters for Markovian jump linear systems. IEEE Transactions on Automatic Control 2006; 51(11):1837-1841.
3. Hu L, Shi P, Frank PM. Robust sampled-data control for Markovian jump linear systems. Automatica 2006; 42(11):2025-2030.
4. Ji YD, Chizeck HJ. Controllability, stabilizability, and continuous-time Markovian jump linear quadratic control. IEEE Transactions on Automatic Control 1990; 35(7):777-788.
5. ∞ control of uncertain Markovian jump systems with mixed neutral, discrete and distributed time-delays. IEEE Transactions on Circuits and Systems I: Regular Papers 2011; 58(8):1910-1923.
6. ∞ filtering for nonlinear stochastic systems with uncertainties and Markov delays. Automatica 2012; 48(1):1159-1166.
7. Mahmoud MS. Interconnected jumping time-delay systems: mode-dependent decentralized stability and stabilization. International Journal of Robust and Nonlinear Control 2012; 22(7):808-826.
8. Karan M, Shi P, Kaya Y. Transition probability bounds for the stochastic stability robustness of continuous- and discrete-time Markovian jump linear systems. Automatica 2006; 42(12):2159-2168.
9. ∞ control of networked control systems with random time delays in both forward and backward communication links. Automatica 2011; 47(4):754-760.
10. Wang Z, Qiao H, Burnham K. On stabilization of bilinear uncertain time-delay stochastic systems with Markovian jumping parameters. IEEE Transactions on Automatic Control 2002; 47(4):640-646.
11. Yu J, Wang L, Yu M. Switched system approach to stabilization of networked control systems. International Journal of Robust and Nonlinear Control 2011; 21(17):1925-1946.
12. Hou Z, Luo J, Shi P, Nguang SK. Stochastic stability of Itô differential equations with semi-Markovian jump parameters. IEEE Transactions on Automatic Control 2006; 51(8):1383-1387.
13. Huang J, Shi Y. Stochastic stability of semi-Markov jump linear systems: an LMI approach. Proc. IEEE Conf. Decision Control and European Control Conf. Orlando, FL, USA, 12-15 December 2011; 4668-4673.
14. Li F, Zhang X. A delay-dependent bounded real lemma for singular LPV systems with time-variant delay. International Journal of Robust and Nonlinear Control 2012; 22(5):559-574.
15. ∞ filtering for singular LPV systems with time variant delay. International Journal of Innovative Computing, Information and Control 2013; 9(1):339-353.
16. Liu Q, Wang W, Wang D. New results on model reduction for discrete-time switched systems with time delay. International Journal of Innovative Computing, Information and Control 2012; 8(5(A)):3431-3440.
17. Su X, Shi P, Wu L, Song Y. A novel approach to filter design for T-S fuzzy discrete-time systems with time-varying delay. IEEE Transactions on Fuzzy Systems 2012; 20(6):1114-1129.
18. Su X, Shi P, Wu L, Song Y. A novel control design on discrete-time Takagi-Sugeno fuzzy systems with time-varying delays. IEEE Transactions on Fuzzy Systems. DOI: 10.1109/TFUZZ.2012.2. 226941.
19. Yang R, Shi P, Liu G, Gao H. Network-based feedback control for systems with mixed delays based on quantization and dropout compensation. Automatica 2011; 47(12):2805-2809.
20. Yang R, Shi P, Liu G. Filtering for discrete-time networked nonlinear systems with mixed random delays and packet dropouts. IEEE Transactions on Automatic Control 2011; 56(11):2655-2660.
21. Zhang G, Han C, Guan Y, Wu L. Exponential stability analysis and stabilization of discrete-time nonlinear switched systems with time delays. International Journal of Innovative Computing, Information and Control 2012; 8(3(A)):1973-1986.
22. Boukas EK, Liu Z, Shi P. Delay-dependent stability and output feedback stabilisation of Markov jump system with time-delay. IEE Proceedings-Control Theory and Applications 2002; 149(5):379-386.
23. Shi P, Boukas EK, Agarwal R. Control of Markovian jump discrete-time systems with norm bounded uncertainty and unknown delay. IEEE Transactions on Automatic Control 1999; 44(1):2139-2144.
24. Shi Y, Yu B. Output feedback stabilization of networked control systems with random delays modeled by Markov chains. IEEE Transactions on Automatic Control 2009; 54(7):1668-1674.
25. Yue D, Han Q. Delay-dependent exponential stability of stochastic systems with time-varying delay, nonlinearity, and Markovian switching. IEEE Transactions on Automatic Control 2005; 50(2):217-222.
26. ∞ control of uncertain Markovian jump systems with time-delay. IEEE Transactions on Automatic Control 2000; 45(1):77-83.
27. Shi P, Xia Y, Liu G, Rees D. On designing of sliding-mode control for stochastic jump systems. IEEE Transactions on Automatic Control 2006; 51(1):97-103.
28. Wu L, Shi P, Gao H. State estimation and sliding mode control of Markovian jump singular systems. IEEE Transactions on Automatic Control 2010; 55(5):1213-1219.
29. ∞ control and filtering for uncertain Markovian jump systems with time-varying delays. IEEE Transactions on Circuits and Systems I: Regular Papers 2007; 54(9):2070-2077.
30. ∞ filtering for 2D Markovian jump systems. Automatica 2008; 44(7):1849-1858.
31. 2 control of Markovian jump systems with uncertain switching probabilities. International Journal of Systems Science 2009; 40(3):255-265.
32. ∞ filtering for uncertain Markovian jump systems with mode-dependent time delays. IEEE Transactions on Automatic Control 2003; 48(5):900-907.
33. Fei Z, Gao H, Shi P. New results on stabilization of Markovian jump systems with time delay. Automatica 2009; 45(10):2300-2306.
34. Gao H, Fei Z, Lam J, Du B. Further results on exponential estimates of Markovian jump systems with mode-dependent time-varying delays. IEEE Transactions on Automatic Control 2011; 56(1):223-229.
35. Yue D, Tian EG, Zhang Y. A piecewise analysis method to stability analysis of linear continuous/discrete systems with time-varying delay. International Journal of Robust and Nonlinear Control 2009; 19(13):1493-1518.
36. Li H, Zhao Q. Reliability evaluation of fault tolerant control with a semi-Markov fault detection and isolation model. Processing IMechE: Journal of Systems and Control Engineering 2006; 220:329-338.
37. Limnios N, Ouhbi B, Sadek A. Empirical estimator of stationary distribution for semi-Markov processes. Communications in Statistics-Theory and Methods 2005; 34(4):987-995.
38. Schwartz C. Control of semi-Markov jump linear systems with application to the bunch-train cavity interaction. PhD Thesis, Northwestern University, 2003.