On finite-time stochastic stability and stabilization of Markovian jump systems subject to partial information on transition probabilities

Circuits, Systems, and Signal Processing

Volumn 31, Issue 6, 2012, Pages 1973-1983

  Zuo, Zhiqiang ^a   Li, Hongchao ^a   Liu, Yi ^a   Wang, Yijing ^a  

^a TIANJIN UNIVERSITY   (China)

Author keywords

Finite time stochastic stability; Markovian jump systems; Partial information on transition probabilities

Indexed keywords

FINITE TIME INTERVALS; MARKOVIAN JUMP SYSTEMS; MEAN SQUARE; NUMERICAL EXAMPLE; PARTIAL INFORMATION; STABILITY RESULTS; STATE SPACE; STATE TRAJECTORY; STOCHASTIC STABILITY; STOCHASTIC STABILITY AND STABILIZATION; STOCHASTIC STABILIZATION; TRANSITION PROBABILITIES;

MARKOV PROCESSES; PROBABILITY; STOCHASTIC SYSTEMS; SYSTEM STABILITY;

STABILIZATION;

EID: 84868331055     PISSN: 0278081X     EISSN: 15315878     Source Type: Journal    
DOI: 10.1007/s00034-012-9420-3     Document Type: Article

References (24)

1. F. Amato, M. Ariola, Finite-time control of discrete-time linear systems. IEEE Trans. Autom. Control 50(5), 724-729 (2005)
2. F. Amato, M. Ariola, P. Dorato, Finite-time control of linear systems subject to parametric uncertainties and disturbances. Automatica 37(9), 1459-1463 (2001)
3. F. Amato, M. Ariola, C. Cosentino, Finite-time stabilization via dynamic output feedback. Automatica 42(3), 337-342 (2006)
4. R. Bellman, Stability Theory of Differential Equations (McGraw-Hill, New York, 1953)
5. S.P. Bhat, D.S. Bernstein, Finite-time stability of continuous autonomous systems. SIAM J. Control Optim. 38(3), 751-766 (2000)
6. E.K. Boukas, Stochastic Switching System: Analysis and Design (Birkhäuser, Boston, 2005)
7. E.K. Boukas, Z.K. Liu, Deterministic and Stochastic Time Delay Systems (Birkhäuser, Boston, 2002)
8. Y.Y. Cao, J. Lam, Robust H∞ control of uncertain Markovian jumping systems with time-delay. IEEE Trans. Autom. Control 45(1), 77-83 (2000)
9. J.R. Chen, F. Liu, Robust reliable H∞ control for discrete-time Markov jump linear systems with actuator failures. J. Syst. Eng. Electron. 19(5), 965-973 (2008)
10. J.X. Dong, G.H. Yang, Robust H2 control of continuous-time Markov jump linear systems. Automatica 44(5), 1431-1436 (2008)
11. P. Dorato, Short-time stability. IRE Trans. Autom. Control 6(1), 86 (1961)
12. M. Karan, P. Shi, C.Y. Kaya, Transition probability bounds for the stochastic stability robustness of continuous- and discrete-timeMarkovian jump linear systems. Automatica 42(12), 2159-2168 (2006)
13. N.N. Krasovskii, E.A. Lidskii, Analysis design of controller in systems with random attributes-Part 1. Autom. Remote Control 22, 1021-1025 (1961)
14. J.L. Liang, J. Lam, Z. Wang, State estimation for Markov-type genetic regulatory networks with delays and uncertain mode transition rates. Phys. Lett. A 373(47), 4328-4337 (2009)
15. M. Liu, D.W.C. Ho, Y. Niu, Stabilization ofMarkovian jump linear system over networks with random communication delay. Automatica 45(2), 416-421 (2009)
16. P. Shi, E.K. Boukas, R.K. Agarwal, Control of Markovian jump discrete-time systems with norm bounded uncertainty and unknown delay. IEEE Trans. Autom. Control 44(11), 2139-2144 (1999)
17. Y. Xia, E.K. Boukas, P. Shi, J. Zhang, Control for discrete singular hybrid systems. Automatica 44(10), 2635-2641 (2008)
18. Y. Xia, J. Zhang, E.K. Boukas, Stability and stabilization of continuous-time singular hybrid systems. Automatica 45(6), 1504-1509 (2009)
19. L.X. Zhang, H∞ estimation for piecewise homogeneous Markov jump linear systems. Automatica 45(11), 2570-2576 (2009)
20. L.X. Zhang, E.K. Boukas, Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities. Automatica 45(2), 436-468 (2009)
21. L.X. Zhang, E.K. Boukas, Mode-dependent H∞ filtering for discrete-time Markovian jump linear systems with partly unknown transition probabilities. Automatica 45(6), 1462-1467 (2009)
22. L.X. Zhang, E.K. Boukas, H∞ control for discrete-time Markovian jump linear systems with partly unknown transition probabilities. Int. J. Robust Nonlinear Control 19(8), 868-883 (2009)
23. L.X. Zhang, E.K. Boukas, J. Lam, Analysis and synthesis of Markov jump linear systems with timevarying delays and partially known transition probabilities. IEEE Trans. Autom. Control 53(10), 2458-2464 (2009)
24. Y. Zhang, Y. He, M. Wu, J. Zhang, Stabilization for Markovian jump systems with partial information on transition probability based on free-connection weighting matrices. Automatica 47(1), 79-84 (2011)