Convex conditions for robust stability analysis and stabilization of linear aperiodic impulsive and sampled-data systems under dwell-time constraints

TL;DR

This paper develops convex conditions for the robust stability and stabilization of linear impulsive and sampled-data systems under dwell-time constraints, using hybrid Lyapunov functions and addressing both periodic and aperiodic cases.

Contribution

It introduces non-conservative convex stability and stabilization criteria for impulsive and sampled-data systems with dwell-time constraints, extending to uncertain systems and broad classes of controllers.

Findings

Convex stability conditions for periodic impulsive systems.

Extension to aperiodic impulsive systems with dwell-time constraints.

Application to robust stabilization of uncertain sampled-data systems.

Abstract

Stability analysis and control of linear impulsive systems is addressed in a hybrid framework, through the use of continuous-time time-varying discontinuous Lyapunov functions. Necessary and sufficient conditions for stability of impulsive systems with periodic impulses are first provided in order to set up the main ideas. Extensions to stability of aperiodic systems under minimum, maximum and ranged dwell-times are then derived. By exploiting further the particular structure of the stability conditions, the results are non-conservatively extended to quadratic stability analysis of linear uncertain impulsive systems. These stability criteria are, in turn, losslessly extended to stabilization using a particular, yet broad enough, class of state-feedback controllers, providing then a convex solution to the open problem of robust dwell-time stabilization of impulsive systems using hybrid stability criteria. Relying finally on the representability of sampled-data systems as impulsive systems, the problems of robust stability analysis and robust stabilization of periodic and aperiodic uncertain sampled-data systems are straightforwardly solved using the same ideas. Several examples are discussed in order to show the effectiveness and reduced complexity of the proposed approach.