Sliding Mode Observer Design For T-S Fuzzy Descriptor Systems With Time Delay

In practice,most control systems are nonlinear.By using T-S fuzzy model,the nonlinear systems can be approximated by multiple local linear systems.T-S fuzzy model has become an effective tool to study nonlinear systems.Descriptor fuzzy model can express the realtime parameter perturbations of the systems more clearly.At the same time,many practical systems such as restricted robots,nuclear reactors,non-causal systems can only be described by descriptor systems.T-S fuzzy descriptor systems describe a class of a wider range of systems.In addition,the sliding mode observer is similar to the sliding mode control strategy,and it has complete robustness to the matched uncertainties or nonlinearities,fast response and simple physical implementation.Therefore,the in-depth study of T-S fuzzy descriptor systems and sliding mode observer has great theoretical significance and application prospects.In recent years,many scholars have studied the T-S fuzzy descriptor systems and sliding mode observer.However,the research results,which relate to the sliding mode observer design for T-S fuzzy descriptor systems,are still very few.In this paper,we will propose a robust H? sliding mode observer design method and a robust adaptive sliding mode observer design method for a class of T-S fuzzy descriptor systems with time-varying delay.The main research works are as follows:1.By considering a class of T-S fuzzy descriptor systems with time-varying delay,a robust H? sliding mode observer design method is proposed.It is well known that the sliding mode control strategy has complete robustness for matched uncertainties or nonlinearities.That is,the sliding mode observer also has above characteristics.Therefore the sliding mode observer has great significance to practical applications.In this paper,firstly,we describe the control systems which will be studied and design a sliding mode observer.Then an integral type switching surface function is designed for the error system,and a delay dependent sufficient condition is proposed such that the sliding mode dynamics are admissible with Hoo performance.Secondly,we design a sliding mode controller.In this part,by using the condition that the fast subsystem of the descriptor system is observable,the error e(t)can be replaced with the output error ey(t)=Ce(t)such that the state feedback sliding mode control law and reachability condition can be guaranteed.Finally,we utilize simulation examples to show the effectiveness of our method.2.By considering a class of T-S fuzzy descriptor systems with time-varying delay,a robust adaptive sliding mode observer design method is proposed.In this paper,we first describe the control system which will be studied and design a sliding mode observer.Then,we consider LiCe(t)into the sliding mode surface function and design an integral switching surface function for the error system.The second is to design a suitable Lyapunov-Krasovskii functional,and some delay dependent sufficient conditions are proposed such that the sliding mode dynamics are admissible with Hoo performance.In addition,we design an adaptive sliding mode controller.In this part,we do not need to using the condition that the fast subsystem of the descriptor is observable,but using a constructed matrix such the reachability condition can be guaranteed.Meanwhile,the requirements of the derivative term matrix and the output matrix can be reduced.Finally,we utilize simulation examples to show the effectiveness of our method.3.By considering the designed robust adaptive sliding mode observer,an observer based sliding mode controller design method is proposed,such that the state feedback control of the original system can be guaranteed.Finally,simulation examples are utilized to demonstrate the effectiveness of our proposed method.