Further results on input-to-state stability for nonlinear systems with delayed feedbacks

• Published in: Automatica (Oxford) Vol. 44; no. 9; pp. 2415 - 2421
• Main Authors: Mazenc, Frédéric, Malisoff, Michael, Lin, Zongli
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.09.2008; Elsevier
• Subjects: Applied sciences; Computer Science; Computer science; control theory; systems; Control system analysis; Control theory. Systems; Delayed systems; Exact sciences and technology; Input-to-state stability; Lyapunov function constructions; Modelling and identification; Other; Input-to-state stability; Lyapunov function constructions; Delayed systems; Closed feedback; Input to state stability; Non linear control; Feedback regulation; Delay system; System identification; Actuator; Lyapunov function; DELAYED SYSTEMS INPUT-TO-STATE STABILITY LYAPUNOV FUNCTION CONSTRUCTIONS SYSTEME DE CONTROLE NON LINEAIRE SYSTEME DIFFERE
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2008.01.024

We consider a class of nonlinear control systems for which stabilizing feedbacks and corresponding Lyapunov functions for the closed-loop systems are available. In the presence of feedback delays and actuator errors, we explicitly construct input-to-state stability (ISS) Lyapunov–Krasovskii functionals for the resulting feedback delayed dynamics, in terms of the available Lyapunov functions for the original undelayed dynamics, which establishes that the closed-loop systems are input-to-state stable (ISS) with respect to actuator errors. We illustrate our results using a generalized system from identification theory and other examples.