Robust reliable H∞ control for uncertain stochastic spatial-temporal systems: The output feedback case

Abstract

This paper is concerned with the robust reliable H∞ output-feedback control problem for a class of uncertain spatial-temporal systems. The system under consideration resides in a given discrete rectangular region and its states evolve not only over time but also over space. A set of sensors located at the specified points is used to measure the system outputs. Based on the available measurement outputs, the static output feedback control strategy is adopted where both the parameter uncertainties and the actuator failures are taken into account. By reorganizing the state variables, we first transform the closed-loop spatial-temporal system into an ordinary differential dynamic system. Then, by dint of the Lyapunov stability theory, a sufficient condition is given that ensures the globally asymptotical stability as well as the H∞ performance requirement for all the possible uncertainties and actuator failures. According to the performance analysis, the desired robust reliable H∞ controller is designed in terms of a matrix inequality which can be solved by available software. Finally, a numerical example is employed to demonstrate the effectiveness of the control scheme proposed.