Uniform Input-to-State Stability for Switched and Time-Varying Impulsive Systems
Provides a unified theoretical framework for ISS analysis of complex dynamical systems, benefiting control theorists and engineers working on stability of hybrid systems.
The paper develops a Lyapunov-based method to establish uniform input-to-state stability (ISS) for time-varying impulsive systems, generalizing existing results to a broader class of systems including switched and nonswitched, impulsive and nonimpulsive cases.
We provide a Lyapunov-function-based method for establishing different types of uniform input-to-state stability (ISS) for time-varying impulsive systems. The method generalizes to impulsive systems with inputs the well-established philosophy of assessing the stability of a system by reducing the problem to that of the stability of a scalar system given by the evolution of the Lyapunov function on the system trajectories. This reduction is performed in such a way so that the resulting scalar system has no inputs. Novel sufficient conditions for ISS are provided, which generalize existing results for time-invariant and time-varying, switched and nonswitched, impulsive and nonimpulsive systems in several directions.