H∞ Piecewise Control for 2-D Parabolic PDE Systems with Collocated Piecewise Observation

This paper presents a piecewise control scheme to achieve the H∞ exponential stabilization for a type of 2-D parabolic PDE systems with disturbance. The actuators and sensors are assumed to be collocated and reticularly distributed in the same spatial domain and both external disturbance and measurement disturbance are considered. With the collocated distributed piecewise observation, the output feedback piecewise control law is designed. Specifically, the 2-D spatial domain is decomposed into rectangular subdomains in accordance to the distribution of actuators (sensors) and the Lyapunov design approach is applied at each rectangular subdomain to derive the collocated output feedback control law. The output feedback control law is eventually presented in the form of liner matrix inequalities (LMIs) and the H∞ exponential stability of the whole system is proved. The efficiency of the proposed control scheme is verified by the numerical simulation.