On input-to-state stability for nonlinear systems with delayed feedbacks
We analyze a class of nonlinear control systems for which stabilizing feedbacks and corresponding Lyapunov functions are both known. We prove that the closed loop systems are input-to-state stable (ISS) relative to actuator errors when small time delays are introduced in the feedbacks. We explicitly construct ISS Lyapunov-Krasovskii functionals for the resulting feedback delayed dynamics, in terms of the known Lyapunov functions for the original undelayed closed-loop dynamics. We also provide a general result on ISS for cascade systems with delays. We demonstrate the efficacy of our results using a generalized pendulum dynamics and other examples. © 2007 IEEE.
Publication Source (Journal or Book title)
Proceedings of the American Control Conference
Mazene, F., Malisoff, M., & Lin, Z. (2007). On input-to-state stability for nonlinear systems with delayed feedbacks. Proceedings of the American Control Conference, 4804-4809. https://doi.org/10.1109/ACC.2007.4282837