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Stability Analysis and Control of Several Classes of Stochastic Hybrid Systems

Author: YangYing
Tutor: LiJunMin
School: Xi'an University of Electronic Science and Technology
Course: Applied Mathematics
Keywords: Stochastic hybrid systems Multiple Lyapunov function Stability and stabilization in probability Almost sure stability and stabilization Finite time stability and stabilization Hybrid feedback control LMI Uncertainty Coupled generalized Lyapunov equation Non-fragile control Nonlinear H-infinity filtering Robust H-infinity control
Type: PhD thesis
Year: 2009
Downloads: 259
Quote: 1
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Stochastic hybrid systems are the complicated systems that consist of continuous (or discrete) time dynamics, discrete event (or logical) dynamics, randomness, and the interaction among them. Stochastic hybrid systems can provide an effective framework for mathematical modeling and analysis of many complex physical phenomena and practical applications. They have a variety of applications such as economic systems, fault tolerant control systems, flexible manufacturing systems, multiple target tracking, aircraft systems and network control systems etc. Thus, the study of stochastic hybrid systems has important significance both in theory and applications.In this dissertation, stability analysis and control problem of several classes stochastic hybrid systems are studied. The main contributions and original ideas included in the dissertation are summarized as follows.1.The stability and stabilization in probability of a class of stochastic hybrid systems are studied. Multiple Lyapunov techniques are used to derive sufficient conditions for stability in probability of the overall system. The conditions are in linear matrix inequalities form, and can be used to solve stabilization synthesis problem with the method of state parttition. The results are extended to the design of a robust-stabilized state-feedback controller as well. A numerical example shows the effectiveness of the proposed approach.2.The almost sure stability and stabilization of a class of stochastic hybrid systems are studied. By using switched Lyapunov techniques, sufficient conditions for almost sure stability are presented and they do not rely on the moment stability of the system. The conditions permit continuous state reset at the switching instant and extend the modeling in [95] of Mao. The conditions are then specialized to case of linear systems, to solve the stabilization synthesis problem. Moreover, the control structure appears not only in the shift part but also in the diffusion part of the underlying stochastic subsystem. The results are easily checkable. A numerical example illustrates the effectiveness of the proposed approach.3.The finite time stability and stabilization of a class of stochastic hybrid systems are studied. Multiple Lyapunov techniques are used to derive sufficient conditions for finite-time stochastic stability of the overall system. The results are reduced to feasibi- lity problems involving linear matrix inequalities(LMIs). Furthermore, based on the state partition of continuous parts of systems, hybrid state feedback controllers which stabilize the closed loop nonlinear and linear systems in the finite-time sense, are then addressed respectively. Moreover, the controller appears not only in the shift part but also in the diffusion part of the underlying stochastic subsystem. A numerical example is presented to illustrate the proposed methodology.4.The problems of stochastic stability and stabilization for a class of discrete-time singular hybrid systems with Markov jump parameters are investigated. Based on multiple Lyapunov function and stochastic generalized Lyapunov function techniques, a necessary and sufficient condition is derived without using the restricted equivalent property of singular systems. The condition is given in terms of coupled generalized Lyapunov equations (CGLEs) such that the solution of the discrete-time singular hybrid systems is stochastic stable with time-homogenous finite state Markov chain. The equations can be solved out by changing into strict linear matrix inequalities (SLMIs). The result is extended to solve stabilization problem and the design of robust state-feedback controller and nonfragile controller. A numerical example shows the effectiveness of the proposed approach.5. The robust H-infinity filtering and control problem for stochastic hybrid systems are discussed. First, the robust H-infinity estimation for nonlinear perturbed stochastic hybrid systems is investigated. We assume that the state and measurement are corrupted by uncertain exogenous disturbances. The H-infinity filter can be abtained by solving second-order nonlinear Hamilton-Jacobi inequalities. Then, multiple Lyapunov techniq- ues are used to derive some important sufficient conditions for the robust stability in probability of the linear stochastic hybrid systems. Furthermore, by analyzing the robust H-infinity performance of the system with the help of the linear matrix inequality(LMI) method, the state feedback matrix and the impulsive control matrix of the system are obtained, and then a robust H-infinity control rule is derived. Finally, a robust H-infinity control design method based on MATLAB software is presented, and a numerical example shows the effectiveness of the proposed approach.

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