Reduced‐order observer‐based controller design for quasi‐one‐sided Lipschitz nonlinear systems with time‐delay

• Published in: International journal of robust and nonlinear control Vol. 31; no. 3; pp. 817 - 831
• Main Authors: Dong, Wenqiang, Zhao, Yanbin, Cong, Yuhao
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 01.02.2021
• Subjects: Control systems design; Controllers; Delay; Design; Feedback control; Lipschitz condition; Nonlinear control; Nonlinear systems; nonlinear time‐delay systems; Parameters; quasi‐one‐sided Lipschitz condition; reduced‐order observer; reduced‐order observer‐based controller; separation principle; State feedback
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.5312

Summary In this article, the problem of reduced‐order observer‐based controller design for a class of nonlinear time‐delay systems is addressed. First, we present sufficient conditions for the existence of the reduced‐order observer of nonlinear time‐delay systems. Then, a state feedback controller is designed to stabilize the systems. Furthermore, it is shown that the separation principle holds for stabilization of the systems based on the reduced‐order observer‐based controller. When the nonlinear part of systems satisfies the quasi‐one‐sided Lipschitz condition, the reduced‐order observer and feedback controller can be designed separately even though the parameter (A, C) of systems is not detectable and parameter (A, B) is not stabilizable. Finally, a numerical example is presented to show the effectiveness of the proposed approach.