A looped-functional approach for robust stability analysis of linear impulsive systems

TL;DR

This paper introduces a novel looped-functional method for analyzing the robust stability of linear impulsive systems, simplifying conditions and broadening applicability compared to existing techniques.

Contribution

It develops a new functional-based approach using looped-functionals, enabling stability analysis without exponential terms and applicable to a wider class of impulsive systems.

Findings

LMIs conditions without exponential terms

Effective for both certain and uncertain systems

Applicable to sampled-data systems

Abstract

A new functional-based approach is developed for the stability analysis of linear impulsive systems. The new method, which introduces looped-functionals, considers non-monotonic Lyapunov functions and leads to LMIs conditions devoid of exponential terms. This allows one to easily formulate dwell-times results, for both certain and uncertain systems. It is also shown that this approach may be applied to a wider class of impulsive systems than existing methods. Some examples, notably on sampled-data systems, illustrate the efficiency of the approach.