NDLI: Stability of random affine systems

Content Provider	IEEE Xplore Digital Library
Author	Zhaojing Wu Xuejun Xie
Copyright Year	2014
Description	Author affiliation: Sch. of Math. & Informational Sci., Yantai Univ., Yantai, China (Zhaojing Wu) \|\| Inst. of Autom., Qufu Normal Univ., Qufu, China (Xuejun Xie)
Abstract	This paper considers the nonlinear systems with stochastic processes whose second-order moments are bounded. The existence and uniqueness of solution are analyzed in global and local sense, respectively. The notions of stability are defined in several manners: asymptotic stability in the mean and in probability of equilibrium, and noise-to-state stability in the mean and in probability of systems. The corresponding criteria are presented by the aid of Lyapunov function methods. Compared with the existing references, only locally Lipschitz conditions are proposed for vector fields, and the smoothness of Lyapunov function are required. These criteria are applied to control problems such as stabilization, regulation and tracking. Although researches of Itô differential equations cover the most fields in the theory and application of stochastic systems, some other models may be more suitable for some specific situations, for example, some practical controls in engineering. The constructed framework is different from that for SDEs, because we mainly fucose our attentions on the control problems of mechanic systems in a stochastic medium with stationary statistic properties.
Starting Page	5317
Ending Page	5321
File Size	124889
Page Count	5
File Format	PDF
ISBN	9789881563873
ISSN	19341768
DOI	10.1109/ChiCC.2014.6895846
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2014-07-28
Publisher Place	China
Access Restriction	Subscribed
Rights Holder	TCCT, CAA
Subject Keyword	Asymptotic stability Stability criteria Stochastic processes Differential equations Lyapunov stability Nonlinear systems Lyapunov methods Random differential equations
Content Type	Text
Resource Type	Article

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