Performance analysis of reset control systems

In this paper we present a general linear matrix inequality-based analysis method to determine the performance of a SISO reset control system in both the 2 gain and 2 sense. In particular, we derive convex optimization problems in terms of LMIs to compute an upperbound on the 2 gain performance and the 2 norm, using dissipativity theory with piecewise quadratic Lyapunov functions. The results are applicable to for all LTI plants and linear-based reset controllers, thereby generalizing the available results in the literature. Furthermore, we provide simple though convincing examples to illustrate the accuracy of our proposed 2 gain and 2 norm calculations and show that, for an input constrained 2 problem, reset control can outperform a linear controller designed by a common nonlinear optimization method.