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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.
93E15Stochastic stability
93D30Scalar and vector Lyapunov functions
93E03General theory of stochastic systems
[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, No. 6, 1758-1777 (1996) · Zbl 0843.93076 · doi:10.1137/S0363012992238679
[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 · doi:10.1016/0022-247X(77)90002-6
[3]Feng, W.; Zhang, J. -F.: Stability analysis and stabilization control of multi-variable switched stochastic systems, Automatica 42, No. 1, 169-176 (2006) · Zbl 1121.93370 · doi:10.1016/j.automatica.2005.08.016
[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, No. 4, 470-482 (2004)
[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.: Stochastic differential equations, Undergraduate mathematical sciences series 22 (2008)
[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, No. 4, 665-670 (2001) · Zbl 1001.93065 · doi:10.1109/9.917674
[11]Loève, M.: Probability theory, vol. 1, Graduate texts in mathematics (GTM) 45 (1977)
[12]Narenda, K. S.; Balakrishnan, J.: A common Lyapunov function for stable LTI systems with commuting A-matrices, IEEE transactions on automatic control 39, No. 12, 2469-2471 (1994) · Zbl 0825.93668 · doi:10.1109/9.362846
[13]Xie, G.; Wang, L.: Controllability and stabilizability of switched linear-systems, Systems and control letters 48, 135-155 (2003) · Zbl 1134.93403 · doi:10.1016/S0167-6911(02)00288-8