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Stability Analysis of Uncertain Stochastic Nonlinear Systems with Time-delays

Author: CuiHongYan
Tutor: GaoCunChen
School: Ocean University of China
Course: Operational Research and Cybernetics
Keywords: stochastic systems time delays linear matrix inequality Lyapunov function robust stability
CLC: TP13
Type: Master's thesis
Year: 2011
Downloads: 44
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Abstract


In most of real engineering systems, it is almost impossible that the accurate mathematics model for the controlled plant is obtained since the uncertainty and nonlinear of the system is existent more or less. The uncertainty mathematics model may more factually describe the real nonlinear control system with time-delays and depict parameter perturbation and external disturbance of the system. Therefore, the research on robust stability for uncertain stochastic nonlinear systems is significant in both theory and practice.Based on Lyapunov stability theory of stochastic systems, linear matrix inequality theory, Lyapunov-Krasovskii stability theory, Analysis of uncertain stochastic and stochastic control Lyapunov function approach, the robust stability and stabilization of nonlinear stochastic are discussed in this dissertation.First it studies mean square delay-dependent exponentially stable of uncertain stochastic systems. First with the help of linear matrix inequality theory and Lyapunov function, and taking full advantage of diffusion in the system, an algebraic criterion of delay-dependent exponentially stability is established for uncertain stochastic time-varying systems, which makes the uncertain stochastic systems with delays be robust exponentially stable in the mean square. Then the effectiveness and the feasibility of the main results are illustrated in this paper by a numerical example.Then it deals with the problem of stochastic robust asymptotically stability for a class of uncertain stochastic nonlinear time-varying systems with time-delays. The parametric uncertainties are assumed to be time-varying and norm bounded. The time-delay factors are unknown and time-varying with known bounds. The aim of this paper is to design a memoryless state feedback control law such that the closed-loop system is stochastically asymptotical stable in the mean square for all admissible parameter uncertainties. A new sufficient condition for the existence of such controllers is presented based on the linear matrix inequality (LMI) approach. Numerical example is given to illustrate the effectiveness of the developed method.Almost surely asymptotic stability of the trivial solution of linear stochastic system with time-delay is discussed; and it is extended to the nonlinear stochastic large-scale system with multi-time-delay. Then, an algebraic criterion of the almost surely asymptotic stability is established for the nonlinear stochastic large-scale system with multi-time-delay. The effectiveness and the feasibility of the main results are illustrated in this paper by a numerical example.This paper deals with the problem of stochastic robust asymptotically stability for a class of uncertain stochastic time-varying systems with time-delays. The systems are based on a new time-delay model proposed recently, which contains multiple successive delay components in the state. It studies the robust stability of the system and gets less conservative stability criteria of it. It can be further explored into the issue with a delay to discuss the stability of the system’s other problems. Can be extended to include several additional variables of uncertain stochastic delay system, its practical significance will be even greater. Numerical example is given to illustrate the effectiveness of the developed method.

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