Sliding Mode Observer Design For T-S Fuzzy Singular System

The singular system that is described by the differential algebraic equations can represent a more wider class of dynamic model than the regular system that is described by the dynamic differential equations.Practically,the singular models can be showed as a large class of complex systems,such as mechanical,bio-economic,chemical and electrical systems and so all.T-S fuzzy singular system is based on the combination of T-S fuzzy system and singular system.The study of T-S fuzzy singular system can solve the global nonlinear singular system model by applying analysis and control method of linear system.It opens up a new way for the study of nonlinear singular systems.Therefore,it is more significative to research the T-S fuzzy singular model in control field.During the past decades,it is proven that the sliding mode control(SMC)theory is an effective approach to cope the nonlinearities and disturbance by choosing appropriate sliding mode surface and using the equivalent control.The SMC is shown to be insensitive to external disturbance signals which are implicit in the input of the system.Sliding mode observer(SMO)is a combination of sliding mode control theory and observer design.The main contents of this paper is as follows:1.It introduces the development and application of fuzzy control theory,singular system,T-S fuzzy singular system and sling mode control.2.It gives out the continuous-time and discrete-time T-S fuzzy singular model which will be studied,and introduces some definitions and lemmas to be used for the development of the main results throughout this paper.3.When the premise variables is measurable,an approach is presented for the design of robust sliding mode observer(SMO)for the Takagi-Sugeno(T-S)fuzzy singular system where the nonlinear function and disturbance are considered.Sufficient conditions using linear matrix inequality(LMI)are derived with the Lyapunov method,which can guarantee the asymptotical stability and robust performance of the estimation error dynamics system on the sliding mode surface and compute the parameter matrices of observer gain.4.The design of SMO for T-S singular system with unmeasurable premise variables is addressed.Linear matrix inequality(LMI)is used to derive sufficient conditions with the Lya-punov method,which can guarantee the asymptotical convergence and robust performance of the sliding mode dynamic estimation error system on the sliding mode surface.