Robust stability of a class of uncertain discrete-time switched systems with time-delay

This paper deals with the robust stability of a class of uncertain discrete-time switched systems with time-delay. The uncertainty considered here is linear fractional uncertainty. Combined the switched Lyapunov-Krasovskii function method with Finsler´s lemma, a new condition in terms of linear matrix inequality (LMI) is presented for the system to be robust asymptotically stable. The proposed analysis method allows extra degree of freedom for stability analysis and control design. A numerical example demonstrates the effect of the proposed approach