Reliable fuzzy output feedback control of nonlinear parabolic distributed parameter systems with sensor faults1

Abstract

This paper studies the problem of output feedback control for a class of nonlinear spatially distributed systems described by parabolic partial differential equations (PDEs) with Markovian jumping sensor faults. The nonlinear parabolic distributed parameter systems (DPSs) are firstly expressed by T-S fuzzy models with parameter uncertainties and the aim is to design a reliable distributed fuzzy static output feedback (SOF) Proportional-spatial Derivative (P-sD) controller guaranteeing the robust stochastic exponential stability of the resulting closed-loop system. Based on a Markovian Lyapunov functional, a descriptor system approach is developed for reliable fuzzy SOF P-sD controller synthesis for the underlying nonlinear parabolic DPSs. It is shown that the controller gains can be obtained by solving a set of finite linear matrix inequalities. Finally, an example is given to illustrate the effectiveness of the proposed method.