Mean Stability of Positive Markov Jump Linear Systems With Homogeneous and Switching Transition Probabilities

IEEE Transactions on Circuits and Systems II: Express Briefs

Volumn 62, Issue 8, 2015, Pages 801-805

  Lian, Jie ^a   Liu, Jiao ^a   Zhuang, Yan ^a  

^a DALIAN UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Copositive Lyapunov function; homogeneous and switching transition probabilities (TPs); mean stability; positive Markov jump linear systems (PMJLSs); time dependent switching

Indexed keywords

LINEAR SYSTEMS; LYAPUNOV FUNCTIONS; MARKOV PROCESSES; SWITCHING;

COPOSITIVE; DISCRETE TIME-DOMAIN; HOMOGENEOUS TRANSITION; LYAPUNOV FUNCTION APPROACHES; MARKOV JUMP LINEAR SYSTEMS; SUFFICIENT AND NECESSARY CONDITION; SWITCHING TRANSITIONS; TIME DEPENDENT;

SYSTEM STABILITY;

EID: 84938353787     PISSN: 15497747     EISSN: 15583791     Source Type: Journal    
DOI: 10.1109/TCSII.2015.2433371     Document Type: Article

References (25)

1. D. Liberzon, Switching in Systems and Control. Boston, MA, USA: Birkhauser, 2003.
2. H. Lin and P. Antsklis, "Stability and stabilizability of switched linear systems: A survey of recent results," IEEE Trans. Autom. Control, vol. 54, no. 2, pp. 308-322, Feb. 2009.
3. S. Kim, S. Campbell, and X. Liu, "Stability of a class of linear switching systems with time delay," IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 53, no. 2, pp. 384-393, Feb. 2006.
4. L. Long and J. Zhao, "A small-gain theorem for switched interconnected nonlinear systems and its applications," IEEE Trans. Autom. Control, vol. 59, no. 4, pp. 1082-1088, Apr. 2014.
5. H. Lin and J. Antsaklis, "Hybrid dynamical systems: An introduction to control and verification," Found. Trends Syst. Control, vol. 1, no. 1, pp. 1-172, Mar. 2014.
6. N. Krasovskii and E. Lidskii, "Analytical design of controller in systems with random attributes," Autom. Remote Control, vol. 22, pp. 1021-1025, 1961.
7. H. Huang, G. Feng, and X. Chen, "Stability and stabilization of Markovian jump systems with time delay via new Lyapunov functionals," IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 59, no. 10, pp. 2413-2421, Oct. 2012.
8. P. Shi, Y. Yin, and F. Liu, "Robust control on saturated Markov jump systems with missing information," Inf. Sci., vol. 265, May 2014, pp. 123-138.
9. D. Wang, J. Wang, and W. Wang, "H-infinity controller design of networked control systems with Markov packet dropouts," IEEE Trans. Syst., Man, Cybern. A, Syst., Humans, vol. 43, no. 3, pp. 689-697, May 2013.
10. ∞ filtering for discrete-time stochastic Markov jump systems with randomly occurred sensor nonlinearities," Automatica, vol. 50, no. 1, pp. 180-186, Jan. 2014.
11. ∞ filtering for a class of discrete-time Markovian jump systems with switching transition probabilities subject to average dwell time switching," Appl. Math. Comput., vol. 225, no. 1, pp. 278-294, Dec. 2013.
12. P. Bolzern, P. Colaneri, and G. Nicolao, "Markov jump linear systems with switching transition rates: Mean square stability with dwell-time," Automatica, vol. 46, no. 6, pp. 1081-1088, Dec. 2010.
13. L. Farina and S. Rinaldi, Positive Linear Systems: Theory and Applications. New York, NY, USA: Wiley-Interscience, 2000.
14. P. Leenheer and D. Aeyels, "Stabilization of positive linear systems," Syst. Control Lett., vol. 44, no. 4, pp. 259-271, Nov. 2001.
15. X. Liu, L. Wang, W. Yu, and S. Zhong, "Constrained control of positive discrete-time systems with delays," IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 55, no. 2, pp. 193-197, Feb. 2008.
16. Z. Shu, J. Lam, H. Gao, B. Du, and L. Wu, "Positive observers and dynamic output-feedback controlllers for interval positive linear systems," IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 55, no. 10, pp. 3209-3222, Nov. 2008.
17. ∞ model reduction for positive systems," Automatica, vol. 47, no. 7, pp. 1504-1511, Jul. 2011.
18. J. Lian and J. Liu, "New results on stability of switched positive systems: An average dwell-time approach," IET Control Theory Appl., vol. 7, no. 12, pp. 1651-1658, Aug. 2013.
19. P. Bolzern, P. Colaneri, and G. Nicolao, "Stochastic stability of positive Markov jump linear systems," Automatica, vol. 50, no. 4, pp. 1181-1187, Apr. 2014.
20. 1-gain performance analysis and positive filter design for positive discrete-time Markov jump linear systems: A linear programming approach," Automatica, vol. 50, no. 8, pp. 2098-2107, Aug. 2014.
21. X. Liu, W. Yu, and L. Wang, "Stability analysis of positive systems with bounded time-varying delays," IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 56, no. 7, pp. 600-604, Jul. 2009.
22. 2-stabilization of linear discrete-time switched systems with minimum dwell-time constraint," Automatica, vol. 50, no. 3, pp. 976-983, Mar. 2014.
23. ∞ estimation for discrete-time piecewise homogeneous Markov jump linear systems," Automatica, vol. 45, no. 11, pp. 2570-2576, Nov. 2009.
24. O. Costa, M. Fragoso, and R. Marques, Discrete-Time Markov Jump Linear Systems. London, U.K.: Springer-Verlag, 2005.
25. J. Geromel, P. Colaneri, "Stability and stabilization of continuous-time switched linear systems," SIAM J. Control Optim., vol. 45, no. 5, pp. 1915-1930, Dec. 2006.