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 ℒ2 gain and ℋ2 sense. In particular, we derive convex optimization problems in terms of LMIs to compute an upperbound on the ℒ2 gain performance and the ℋ2 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 ℒ2 gain and ℋ2 norm calculations and show that, for an input constrained ℋ2 problem, reset control can outperform a linear controller designed by a common nonlinear optimization method. Copyright © 2009 John Wiley & Sons, Ltd.

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