Static output feedback stabilization for a linear parabolic PDE system with time-varying delay via mobile collocated actuator/sensor pairs

摘要

This paper addresses a static output feedback (SOF) stabilization problem for a linear parabolic partial differential equation (PDE) system with time-varying delay via mobile collocated actuator/sensor pairs. Initially, an SOF stabilization scheme via mobile actuator/sensor pairs is proposed for the delayed PDE system, where the spatial domain is divided into multiple subdomains according to the number of actuator/sensor pairs and the projection modification algorithm is employed to ensure each collocated actuator/sensor pair only can move within the respective subdomain. Subsequently, the well-posedness of the closed-loop delayed PDE system is analyzed using the operator semigroup theory. Then, by constructing an appropriate Lyapunov-Krasovskii functional candidate, a delay-dependent control-plus-guidance design is developed in the form of bilinear matrix inequalities (BMIs), such that the resulting closed-loop system is exponentially convergent and the mobile actuator/sensor guidance can improve the transient response of closed-loop state. Moreover, an iterative algorithm based on linear matrix inequalities is provided to solve the BMIs. Finally, numerical simulations are presented to illustrate the effectiveness of the proposed method. (C) 2020 Elsevier Ltd. All rights reserved.