Stabilization of interconnected nonlinear stochastic Markovian jump systems via dissipativity approach. (English) Zbl 1235.93251

Summary: This paper considers the stabilization problems for interconnected nonlinear stochastic Markovian jump systems from the viewpoint of dissipativity theory. Based on the strongly stochastic passivity theory, the feedback equivalence and global stabilization problems are studied for interconnected nonlinear stochastic Markovian jump systems. The strongly stochastic \(\gamma \)-dissipativity sustains a direct \(H_{\infty }\) control for this class of systems instead of solving coupled Hamilton – Jacobi inequalities.


93E15 Stochastic stability in control theory
60J75 Jump processes (MSC2010)
93C10 Nonlinear systems in control theory
Full Text: DOI


[1] Byrnes, C.I.; Isidori, A.; Willems, J.C., Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear systems, IEEE transactions on automatic control, 36, 11, 1228-1240, (1991) · Zbl 0758.93007
[2] Dragan, V.; Morozan, T.; Stoica, A.M., Mathematical methods in robust control of linear stochastic systems, (2006), Springer New York
[3] Ghaoui, L.E.; Ait Rami, M., Robust state-feedback stabilization of jump linear systems via lmis, International journal of robust and nonlinear control, 6, 1015-1022, (1996) · Zbl 0863.93067
[4] Khalil, H.K., Nonlinear systems, (2002), Prentice-Hall Englewood Cliffs, NJ · Zbl 0626.34052
[5] Lin, Z., & Lin, Y. (2008). State-feedback \(H_\infty\) control for nonlinear stochastic systems with Markovian jumps in infinite time horizon. In Proceedings of the 17th IFAC world congress. Seoul, Korea (pp. 13486-13491).
[6] Lin, Z.; Lin, Y.; Zhang, W., A unified design for state and output feedback \(H_\infty\) control of nonlinear stochastic Markovian jump systems with state and disturbance-dependent noise, Automatica, 45, 2955-2962, (2009) · Zbl 1192.93029
[7] Lin, Z.; Liu, J.; Lin, Y.; Zhang, W., Nonlinear stochastic passivity, feedback equivalence and global stabilization, International journal of robust and nonlinear control, (2011)
[8] Mao, X.; Yuan, C., Stochastic differential equations with Markovian switching, (2006), Imperial College Press London · Zbl 1126.60002
[9] Mariton, M., Jump linear systems in automatic control, (1990), Marcel Dekker New York
[10] Willems, J.C., Dissipative dynamic systems part I: general theory, Archive for rational mechanics, 45, 321-393, (1972)
[11] Zhang, W.; Chen, B.S., State feedback \(H_\infty\) control for a class of nonlinear stochastic systems, SIAM journal on control and optimization, 44, 1973-1991, (2006) · Zbl 1157.93019
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