Analysis And Control For 2-D Discrete Fuzzy Systems

This paper mainly deals with the problem of stability analysis,state-feedback controller,outputfeedback controller for several class of 2-D discrete fuzzy systems.Only using the methods of 1-D systems,many problems of 2-D discrete fuzzy systems which relies on two variables can not be solved.To deal with these problems,different Lyapunov functions on the directions of two variables will be chosen.It can be divided into the following three parts:The first part mainly designs the state-feedback controller for a class of 2-D discrete fuzzy systems,it includes the certainty system and the system with linear fractional uncertainty.The uncertainties of this form contains the norm bounded uncertainties,which has more general significance.The state-feedback controller is designed by introducing a free-weighting matrix,using the Parallel Distributed Compensation methods,and considering the current state and control input as two independent variables,which make the system asymptotic stable.The gains of the state-feedback controller can be obtained via convex optimization techniques.The second part mainly designs the output-feedback controller and H_?output-feedback controller for a class of 2-D discrete fuzzy systems with linear fractional uncertainty.As an important method in the design of control systems,output feedback control are fully investigated in this part.Not only consider the H_?output feedback control for certain systems,we also consider the H_?output feedback control for uncertain systems.The feedback gain matrices are decoupled with the system matrices via the singular value decomposition of matrices.And then,the output feedback controller gains can be obtained by solving a series of matrix inequalities.In this part,the H_?output feedback controller which can achieve the restraint of system disturbances will be designed under the condition that the H_?performance is considered as an important index.The third part mainly designs the H_?state-feedback controller for a class of 2-D discrete stochastic fuzzy systems.The 2-D discrete stochastic fuzzy system under consideration can be regarded as the Fornasini-Marchesini Second Model whose system matrices are extended to stochastic ones.These stochastic matrices stand for the stochastic disturbances imposing on the system matrices.Sufficient conditions of mean-square stability with H_?performance for the 2-D discrete stochastic fuzzy system are established by using method of Lyapunov function and introducing a free-weighting matrix.Finally,it has been shown that via a numerical example the analysis result obtained by Lyapunov function is valid.