Quadratic stability of reset control systems with delays

This paper investigates robust stability of reset control systems with both uncertainties and transmission delays. Firstly, a generalized Lyapunov-Krasovskii theorem is proven. Secondly, the technique of parameter-dependent full-rank right annihilator of matrices is used to deal with the uncertain reset time instants caused by output matrix uncertainties. Based on this, several necessary and sufficient conditions for dissipativeness of reset mappings are established. Finally, some delay-independent and a delay-dependent robust stability results are given in terms of linear matrix inequalities (LMIs) by using certain kind of Lyapunov-Krasovskii functionals. An illustrative example is also given to explain the proposed results.