LMI-based Technique To Robust Control For Delay T-S Fuzzy Descriptor Systems

The descriptor system is more general dynamic system than the normal system.T-S fuzzy descriptor system with time-delay is developed from normal T-S fuzzy system with time-delay combined with the descriptor system theory.It can accurately approximate a nonlinear descriptor system.It is an effective way to solve the control problem of nonlinear descriptor systems.Delays inevitably exist in many practical systems and frequently lead to instability and poor performance.So it has important theoretical significance and practical value for studying T-S fuzzy descriptor systems with time-delay.In this paper,we discuss the following problems on robust control of T-S fuzzy descriptor system with time-delay:Firstly,the passive control problem is studied for T-S fuzzy descriptor systems with timedelay.A sufficient condition is given under which an observer-based controller is solvable.This can guarantee that the closed-loop systems are admissible and strictly passive.Using the theory of matrix magnified,we express the sufficient condition as linear matrix inequality(LMI).Thus,the solution of passive controller can be obtained by solving the LMI.In the case of unknowing states,we solve the problem of passive control for a kind of nonlinear descriptor systems via T-S fuzzy model and give its concrete algorithm.Secondly,the robust H_? control problem is investigated for a kind of nonlinear system via T-S fuzzy descriptor systems.A sufficient condition is obtained under which an observer-based controller is existent for the nonlinear descriptor systems.Basis on the sufficient condition,by using the Lyapunov function method and matrix magnified theory,we express the condition as LMI,which can guarantee that the closed-loop T-S fuzzy descriptor systems with time-delay are admissible and hold the H_? performance to a prescribed disturbance attenuation level.It solves well the robust H_? control problem for nonlinear descriptor systems with time-delay,disturbance and the unknowing states and gives its concrete algorithm.Finally,the observer-based dissipative control problem is solved for a kind of nonlinear descriptor system via a T-S fuzzy model.The observer-based dissipative controllers design method is presented for nonlinear descriptor systems and the ones with time-delay.A sufficient condition is obtained under which an observer-based controller is existent,which can guarantee that the closed-loop T-S fuzzy descriptor systems are admissible and strictly dissipative.Then the condition is expressed as LMI.A sufficient condition and its concrete algorithm are also given for the closed-loop T-S fuzzy descriptor systems with time-delay.The proposed method can well solve the dissipative control problem for a kind of nonlinear descriptor systems with time-delay,disturbance and the unknowing states.