Stability analysis of switched stochastic systems. (English) Zbl 1209.93157

Summary: For a class of Switched Stochastic (SS) systems, the Moment Stability (M-S) and Sample Path Stability (SP-S) are investigated, respectively, and there are two main contributions. First, based on accurate estimations for the powers of solution of a special nonswitched stochastic system, by employing the concepts of a Lyapunov function and describing the switching laws with the average dwell-time and the subsystems, three sufficiency theorems of \(p\)-th M-S are given for the SS systems. Then, for the SP-S of such systems, based on the results of \(p\)-th M-S, two sufficiency theorems are obtained for \(p>2\) and \(p=2\), respectively.


93E15 Stochastic stability in control theory
93D30 Lyapunov and storage functions
93E03 Stochastic systems in control theory (general)
Full Text: DOI


[1] Caines, P.E.; Zhang, J.-F., On the adaptive control of jump parameter systems via nonlinear filtering, SIAM journal on control and optimization, 33, 6, 1758-1777, (1996) · Zbl 0843.93076
[2] Curtain, R.F., Stochastic evolution equations with general white noise disturbance, Journal of mathematical analysis and applications, 60, 570-595, (1977) · Zbl 0367.60067
[3] Feng, W.; Zhang, J.-F., Stability analysis and stabilization control of multi-variable switched stochastic systems, Automatica, 42, 1, 169-176, (2006) · Zbl 1121.93370
[4] Feron, E. (1996). Quadratic stabilizability of switched systems via state and output feedback. Technical report CICS-P-468, MIT.
[5] Giua, A., Seatzu, C., & Van Der Mee, C. (2001). Optimal control of switched autonomous linear systems. In Proc. 40th Conf. Decision and Control (pp. 2472-2477).
[6] Hespanha, J.P., Uniform stability of switched linear systems: extensions of lasalle’s invariance principle, IEEE transactions on automatic control, 49, 4, 470-482, (2004) · Zbl 1365.93348
[7] Hespanha, J.P., & Morse, A.S. (1999). Stability of switched systems with average dwell-time. In Proc. 38th IEEE conf. decision and control (pp. 2655-2660).
[8] Hongzhu, Y., Feiqi, D., Jintang, C., & Yongqing, L. (2000). Direct algebraic criteria for exponential moment stability for linear stochastic systems. In Proc. American control conf. (pp. 3800-3801).
[9] Hu, S.G., (), (in Chinese)
[10] Li, Z.G.; Wen, C.Y.; Soh, Y.C., Stabilization of a class of switched systems via designing switching laws, IEEE transactions on automatic control, 46, 4, 665-670, (2001) · Zbl 1001.93065
[11] Loève, M., ()
[12] Narenda, K.S.; Balakrishnan, J., A common Lyapunov function for stable LTI systems with commuting \(A\)-matrices, IEEE transactions on automatic control, 39, 12, 2469-2471, (1994) · Zbl 0825.93668
[13] Xie, G.; Wang, L., Controllability and stabilizability of switched linear-systems, Systems and control letters, 48, 135-155, (2003) · Zbl 1134.93403
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.