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Study On Stabilization Of Several Nonlinear Stochastic Systems With Time Delay

Posted on:2016-11-17Degree:DoctorType:Dissertation
Country:ChinaCandidate:C R ZhaoFull Text:PDF
GTID:1108330464463467Subject:Applied Mathematics
Abstract/Summary:PDF Full Text Request
Nonlinear, time-delay and external stochastic disturbance are commonly encountered in real systems, and the existence of time-delay is often a significant cause of instability and oscillation. Hence, the study of stochastic nonlinear systems and stochastic time-delay systems has received much attention. In this paper, for stochastic nonlinear systems with inverse dynamics and stochastic nonlinear systems with time-varying delay, the problems of controller design and stability analysis are investigated. The main contributions include:1. For a more general class of stochastic nonlinear systems with stochastic integral inputto-state stability(SiISS) inverse dynamics, we further consider the problem of output feedback control and focus on solving the following problems: 1) a class of counterexamples are reconstructed to discuss the relationship between two small-gain type conditions on SiISS and 2)under the weaker conditions on nonlinearities, based on a reduced-order observer, small-gain type condition on SiISS and stochastic LaSalle theorem, an output feedback controller design method is given.2. For a class of stochastic high-order nonlinear system with time-varying delay, a combined homogeneous domination and sign function design approach is introduced to state feedback control. The use of the combined approach removes the restrictions on system order and relaxes the assumptions on nonlinear functions.3. For a class of stochastic high-order feedforward nonlinear systems with time-varying delay, under the weaker assumptions on nonlinear functions, using the homogeneous domination design method and sign function design technique, constructing an appropriate LyapunovKrasovskii functional, an output feedback controller is constructed to drive the closed-loop system to be globally asymptotically stable in probability.4. For a class of stochastic feedforward nonlinear systems with input and state delay, under a set of coordinate transformations, with the aid of feedback domination technique, choosing an appropriate Lyapunov-Krasovskii functional and scaling gain, a linear output feedback controller is designed to drive the closed-loop system globally asymptotically stable in probability.5. For a class of stochastic nonlinear systems with time-varying delay, we further consider the problem of output feedback stabilization and focus on solving the following problems: 1)Completely remove the slowly varying assumption on time-varying delay, which is frequently used in dealing with system with time-varying delay. 2) Construct a quadratic Lyapunov function, and present an easy way to deal with Hessian term. With the aid of feedback domination technique and the Razumikhin-type theorem, an output feedback controller is designed to drive the closed-loop system globally asymptotically stable in mean square.
Keywords/Search Tags:Stochastic high-order nonlinear systems, Stochastic feedforward nonlinear systems, time-varying delay, state feedback stabilization, output feedback stabilization, reduced-order observer, small-gain method, sign function
PDF Full Text Request
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