Separation principle for quasi‐one‐sided Lipschitz nonlinear systems with time delay

• Published in: International journal of robust and nonlinear control Vol. 30; no. 6; pp. 2430 - 2442
• Main Authors: Hu, Guang‐Da, Dong, Wenqiang, Cong, Yuhao
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 01.04.2020
• Subjects: Control systems design; Feedback control; Lipschitz condition; Nonlinear systems; nonlinear time‐delay systems; observer‐based controller; Parameters; quasi‐one‐sided Lipschitz condition; Separation; separation principle; Stabilization; State feedback; State observers; Time delay systems; Time lag
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.4881

Summary In this article, we address the problem of output stabilization for a class of nonlinear time‐delay systems. First, an observer is designed for estimating the state of nonlinear time‐delay systems by means of quasi‐one‐sided Lipschitz condition, which is less conservative than the one‐sided Lipschitz condition. Then, a state feedback controller is designed to stabilize the nonlinear systems in terms of weak quasi‐one‐sided Lipschitz condition. Furthermore, it is shown that the separation principle holds for stabilization of the systems based on the observer‐based controller. Under the quasi‐one‐sided Lipschitz condition, state observer and feedback controller can be designed separately even though the parameter (A,C) of nonlinear time‐delay systems is not detectable and parameter (A,B) is not stabilizable. Finally, a numerical example is provided to verify the efficiency of the main results.