Reducing conservatism in robust stability analysis and stabilisation of arbitrary switched linear systems

Abstract

Parametric modelling of uncertainties has been considered for switched linear systems in the past few years to improve the efficiency of robust stability analysis. The main goal of this paper is simultaneously alleviating conservatism and computational effort for robust stability analysis and stabilisation of arbitrary switched linear systems with uncertain parameters. For this purpose, stability conditions are revised and some constraints are relaxed. First, an improved weighted stability bound is proposed which is larger than previous results. Since the obtained stability bound depends on the chosen Lyapunov function, an optimisation problem is also given to determine its maximum value. Then, using the stability results, robust stabilisation of parametric uncertain switched linear systems under arbitrary switching is investigated. In this regard, a design method is presented to offer a static state feedback control law. The conservatism of the proposed control law is reduced by relaxing the constraint on upper bound of a matrix variable. Finally, illustrative examples are included to demonstrate the effectiveness of the proposed method.