H2 performance analysis of reset control systems

To overcome fundamental limitations of linear controllers, reset controllers were proposed in literature. Since the closed loop system including such a reset controller is of a hybrid nature, it is difficult to determine its performance. The focus in this paper is to determine the performance of a SISO reset control system in H₂ sense. The method is generally applicable in the sense that it is valid for any proper LTI plant and linear-based reset controller. We derive convex optimization problems in terms of LMIs to compute an upperbound on the H₂ norm, using dissipativity theory with piecewise quadratic Lyapunov functions. Finally, by means of a simple multiobjective tracking example, we show that reset control can outperform a linear controller obtained via a standard multiobjective control design method.