This paper investigates a new optimal control stabilization for continuous switched linear systems under arbitrary switching. In fact, based on the aggregation techniques and the application of the Borne-Gentina stability criterion. New stabilization conditions under arbitrary switching are deduced. These results 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 of the close loop system.
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