H\infty Piecewise Control for Linear Parabolic Distributed Parameter Systems With Piecewise Observation in Space

• Published in: IEEE access Vol. 7; pp. 62865 - 62874
• Main Authors: Liu, Yaqiang, Sun, Changyin
• Format: Journal Article
• Language: English
• Published: IEEE 2019
• Subjects: Actuators; Adaptive control; Aerospace electronics; Attenuation; Closed loop systems; H∞ control; measurement disturbance; non-collocated piecewise observation; parabolic distributed parameter systems; Sensors; Symmetric matrices
• ISSN: 2169-3536; 2169-3536
• DOI: 10.1109/ACCESS.2019.2916993

In this paper, the <inline-formula> <tex-math notation="LaTeX">H_\infty </tex-math></inline-formula> piecewise control problem is discussed for linear parabolic distributed parameter systems (DPSs) with piecewise observation in space. An <inline-formula> <tex-math notation="LaTeX">H_\infty </tex-math></inline-formula> 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 <inline-formula> <tex-math notation="LaTeX">H_\infty </tex-math></inline-formula> performance constraint. Finally, the numerical simulation results of the closed-loop system and the <inline-formula> <tex-math notation="LaTeX">H_\infty </tex-math></inline-formula> attenuation level demonstrate the effectiveness of the proposed method.