H∞ Piecewise Control for Linear Parabolic Distributed Parameter Systems with Piecewise Observation in Space

Abstract

In this paper, the H∞ piecewise control problem is discussed for linear parabolic distributed parameter systems (DPSs) with piecewise observation in space. An H∞ performance constraint is provided in this paper to solve the effect caused by the measurement disturbance. First, a static feedback controller is designed for the collocated piecewise observation in space, then an observer-based dynamic feedback controller is designed for the non-collocated piecewise observation in space. By the Lyapunov technique, it has been proved that if the LMI-based sufficient conditions are fulfilled, the resulting closed-loop systems are exponentially stable under a prescribed H∞ performance constraint. Finally, the numerical simulation results of the closed-loop system and the H∞ attenuation level demonstrate the effectiveness of the proposed method.