Stability analysis and stabilization of switched linear systems based on vector norms approach

The stability analysis and the stabilization problems for continuous-time switched linear systems are studied in this paper, by investigating a new stability conditions based on the comparison, the overvaluing principle, the application of Borne-Gentina criterion and the Kotelyanski conditions. These 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 a regular vector norm 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 for global asymptotic stability.