Stability and stabilisation of reset control systems with uncertain output matrix

The stability analysis of reset control systems is challenging when reset time instants are uncertain, because such uncertainties may damage or even destabilise the system. This study considers reset control systems with uncertain output matrix, and presents sufficient conditions for the quadratic stability and finite gain ℒ₂ stability of the closed-loop reset systems. Then, the results are extended to piecewise quadratic stability, which is much less conservative. The design of the reset controller is also discussed. All the results are given as linear matrix inequalities by using a lemma about multi-convex function. Several examples are given to show the effectiveness of the obtained results.