Output Feedback Stabilization for a Class of Cascade Nonlinear ODE-PDE Systems

• Published in: International journal of control, automation, and systems Vol. 19; no. 7; pp. 2519 - 2528
• Main Authors: Chang, Yanjie, Sun, Tongjun, Zhang, Xianfu, Chen, Xiandong
• Format: Journal Article
• Language: English
• Published: Bucheon / Seoul Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers 01.07.2021; Springer Nature B.V
• Subjects: Control; Control Theory and Applications; Engineering; Feedback control; Mechatronics; Nonlinear systems; Output feedback; Robotics; Stability analysis; Subsystems; Cascade ODE-PDE systems; Lyapunov functional; low gain observer; output feedback
• ISSN: 1598-6446; 2005-4092
• DOI: 10.1007/s12555-020-0402-0

In this paper, the output feedback stabilization problem is studied for a class of cascade nonlinear ODE-PDE systems. The nonlinear terms of ODE-subsystem are assumed to be bounded by a known constant multiplied by unmeasured states, and PDE-subsystem is a diffusion equation. Especially, the unstable diffusion equation is considered. Based on the low gain observer and a series of transformations, the output feedback stabilization problem is converted into designing proper gain parameters. Furthermore, the stability of the closed-loop system is analyzed by Lyapunov theorem. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed control strategy.