A new stability analysis and stabilization of uncertain switched linear systems based on vector norms approach

In the present paper a new stability analysis and stabilization of continuous-time uncertain switched linear systems is considered. This approach is based on the comparison, the overvaluing principle, the application of Borne-Gentina criterion and the Kotelyanski conditions. The stability conditions issued from vector norms correspond to a vector Lyapunov function. Indeed, the switched system to be controlled will be represented in the Companion form. A comparison system relative to regular vector norms is used in order to get the simple arrow form of the state matrix that yields to a suitable use of Borne-Gentina criterion for the establishment of sufficient conditions as function of the uncertain parameters for global asymptotic stability.