On stability analysis of discrete-time uncertain switched nonlinear time-delay systems

This paper addresses the stability analysis problem for a class of discrete-time switched nonlinear time-delay systems with polytopic uncertainties. These considered systems are characterized by delayed difference nonlinear equations which are given in the state form representation. Then, a transformation under the arrow form is employed. Indeed, by constructing an appropriated common Lyapunov function, and also by resorting to the Kotelyanski lemma and the M-matrix proprieties, new delay-independent stability conditions under arbitrary switching law are deduced. Compared with the existing results of switched systems, those obtained results are formulated in terms of the unknown polytopic uncertain parameters, explicit and easy to apply. Moreover, this method allows us to avoid the search for a common Lyapunov function which is a difficult matter. Finally, a numerical example is presented to illustrate the effectiveness of the proposed approach.