Control of non‐linear switched systems with average dwell time: interval observer‐based framework

Abstract

The authors address control system design based on an interval observer for non‐linear switched systems with non‐linear vector functions that are assumed to satisfy Lipschitz conditions. First, the observer gain satisfying a Metzler matrix can be solved by optimisations of linear matrix inequalities (LMIs). Second, an interval observer is designed to estimate the states of non‐linear switched systems with the average dwell time scheme, and sufficient conditions for state estimation are presented in terms of an LMI formulation. Third, based on an interval observer, state feedback matrices are designed to construct an asymptotically stabilising switching controller. Finally, a numerical example is provided to demonstrate the efficiency of the approach.