Robust stability and stabilization studies for uncertain switched systems based on vector norms approach

Abstract

In this paper, we investigate the problems of robust stability and stabilization via a state feedback controller for both continuous and discrete-time switched linear systems with polytopic uncertainties. These considered systems are represented in the state form. Then, a transformation under the arrow form is performed. Thus, based on the construction of a common Lyapunov function associated with the application of the Kotelyanski lemma, the \(M\)—matrix proprieties and the aggregation techniques, new sufficient conditions for robust stability and stabilization under arbitrary switching laws are established. It should be pointed out that the obtained results are explicit, easy to apply and formulated in terms of the polytopic uncertainty parameters. In addition, this proposed method allows us to avoid the search of a common Lyapunov function which is a difficult matter. For illustration, a DC motor model with separate excitation under variable mechanical loads is used to show the effectiveness and the potential of the proposed techniques.