Semi-global Interval Observer-Based Robust Control of Linear Time-Invariant Systems Subject to Input Saturation

• Published in: Circuits, systems, and signal processing Vol. 43; no. 8; pp. 4928 - 4951
• Main Authors: Zhang, Zhipeng, Shen, Jun, Zhang, Jiyuan, Qiu, Hongling
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.08.2024; Springer Nature B.V
• Subjects: Circuits and Systems; Control methods; Control systems; Design parameters; Design techniques; Disturbances; Eigenvalues; Electrical Engineering; Electronics and Microelectronics; Engineering; Feedback control; Instrumentation; Liapunov functions; Riccati equation; Robust control; Signal processing; Signal,Image and Speech Processing; Stability analysis; System theory; Time invariant systems; Input saturation; Low-gain feedback; Parametric Lyapunov equation; Interval observer
• ISSN: 0278-081X; 1531-5878
• DOI: 10.1007/s00034-024-02716-z

This article investigates the issue of robust control based on interval observers for continuous-time linear time-invariant (LTI) systems with input saturation and disturbances. Firstly, an interval observer is derived by resorting to the system’s output information and the interval bounds on the disturbances. Then, a parametric Lyapunov equation (PLE)-based low-gain feedback control method is introduced to guarantee semi-global boundedness. In contrast to the current parametric algebraic Riccati equation (PARE)-based method that requires an iterative approach to solve the PARE online, all relevant parameters in the adopted low-gain design approach are offline determined a priori. Moreover, considering the characteristics of the interval observer, a new stability analysis architecture is given by using a Lyapunov function with a mixture of quadratic and copositive types. Finally, two numerical examples are employed as a means of substantiating the theoretical results.