Robust Output Practical Stability of Time-Varying Nonlinear Control Systems via Indefinite Lyapunov Functions

This paper focuses on studying the problem of robust output practical stability of time-varying nonlinear control systems. The main innovation lies in the fact that the proposed approach for stability analysis allows for the computation of bounds that characterize the asymptotic convergence of solutions to a small ball centered at the origin using a Lyapunov method with a definite derivative. Under different conditions on the perturbation, the authors demonstrate that the system can be globally robustly asymptotically output stable by designing a candidate feedback controller. Finally, three examples are given to illustrate the practical implications and significance of the theoretical results.