Analysis And Synthesis Of Piecewise Linear Systems

In this dissertation,the output feedback stabilization,H_∞control,guaranteed cost control of piecewise linear systems are investigated deeply.In addition, the guaranteed cost controller design fbr a class of nonlinear systems is studied with the corresponding results of piecewise linear systems.The main contributions are as fbllows.Firstly,the approach to the output feedback control fbr uncertain piecewise linear systems withα-stability constraint is presented.To make use of piecewise quadratic Lyapunov functions technique for the perfbrmance analysis of closed-loop augmented systems,the augmented piecewise-continuous quadratic Lyapunov functions are reconstructed.It is shown that the output feedback controller design procedure of uncertain piecewise linear systems withα-stability constraint can be cast as solving a set of bilinear matrix inequalities(BMIs).Secondly,a new mixed algorithm that combines genetic algorithm(GA) and interior-point method is designed fbr solving the BMIs problem which is an NP hard problem.Specifically,some of the variables in BMIs are set to be searched by GA,then the corresponding non-convex problem reduces to the semidefinite programming(SDP)involving LMIs,which is convex and can be solved numerically with available software based on interior-point method.The proposed algorithm can be easy to carry out,and overcomes the shortcomings of the existent algorithms which are hard to converge to the global optimum or are not computationally tractable fbr large scale problems.Thirdly,the design of robust H_∞output feedback controller fbr uncertain piecewise linear systems is presented.By constructing piecewise continuous Lyapunov functions fbr the closed-loop augmented systems,the H_∞output feedback controller design is cast as the feasibility problem of a set of BMIs,and the optimal H_∞controller can be obtained by solving a non-convex optimization problem under the constraints of BMIs.Fourthly,the guaranteed cost control fbr uncertain piecewise linear systems via state feedback and output feedback are investigated respectively based on the piecewise quadratic Lyapunov functions technique and Hamilton-Jacobi-Bellman (H-J-B)inequality method.It has been shown that both the state feedback opti- mal controller and output feedback optimal controller,which minimize the upper bounds on cost function,can be obtained respectively by solving a non-convex optimization problem under the BMIs constraints.The controller obtained can be judged by a lower bound on cost function which can be obtained by SDP.Finally,the optimal state feedback guaranteed cost controller design for the nonlinear systems is presented.The nonlinear systems are described as a class of uncertain piecewise linear systems,then with the results of guaranteed cost controller design for piecewise linear systems,the optimal guaranteed cost controller for the nonlinear systems can be obtained by solving a non-convex optimization problem under the BMIs constraints.