(Integral-)ISS of switched and time-varying impulsive systems based on global state weak linearization

TL;DR

This paper establishes input-to-state stability and integral ISS for nonlinear, time-varying, and switched impulsive systems that admit a global state weak linearization, without requiring dwell-time constraints or linearity under zero input.

Contribution

It introduces a generalized stability analysis framework for impulsive systems with weak linearization, removing several restrictive assumptions from prior work.

Findings

Systems are ISS under small inputs

Systems are also integral ISS

No dwell-time constraints are needed

Abstract

It is shown that impulsive systems of nonlinear, time-varying and/or switched form that allow a stable global state weak linearization are jointly input-to-state stable (ISS) under small inputs and integral ISS (iISS). The system is said to allow a global state weak linearization if its flow and jump equations can be written as a (time-varying, switched) linear part plus a (nonlinear) pertubation satisfying a bound of affine form on the state. This bound reduces to a linear form under zero input but does not force the system to be linear under zero input. The given results generalize and extend previously existing ones in many directions: (a) no (dwell-time or other) constraints are placed on the impulse-time sequence, (b) the system need not be linear under zero input, (c) existence of a (common) Lyapunov function is not required, (d) the perturbation bound need not be linear on the input.