Stability analysis and control synthesis of hybrid time-varying linear systems using a discretization-based approach

Abstract

A strategy for stability analysis and control design concerning a class of hybrid linear time-varying (LTV) systems is proposed in this paper. First, the transition matrix of the system is computed and then used to formulate the stability analysis condition, unifying both the flows and jumps into a single continuous-time framework and resulting in a straightforward methodology for hybrid dynamics. Such condition is then adapted to yield the proposed synthesis techniques, capable of generating a time-varying state-feedback gain to stabilize the hybrid LTV system. A discretization procedure is then proposed for both analysis and synthesis conditions, resulting on a numerically suitable approach that allows the adaptation of any LTV discrete-time synthesis technique to deal with the considered hybrid LTV systems. Finally, to highlight the possibilities of the methodology, the conditions are adapted for the stabilization of sampled-data time-varying systems. Numerical examples illustrate the validity and potentialities of the proposed techniques.