فهرست نشریات علمی دسترسی آزاد ایران

In this paper, a novel approach based on a non-monotonic Lyapunov–Krasovskii functional is first proposed for the comprehensive stability analysis of discrete-time switched systems with time delays in an m-step-ahead scheme. Subsequently, by extending these results, non-uniform robust stability conditions suitable for systems with uncertainties are derived. In this method, the stringent requirement of the uniform decrease of the Lyapunov–Krasovskii functional is replaced by non-monotonic conditions; that is, the functional is allowed to increase at certain steps, while its overall trend must remain decreasing. Consequently, this approach accommodates a broader class of functionals for stability analysis. Within the non-monotonic Lyapunov–Krasovskii framework, a set of sufficient conditions in the form of linear matrix inequalities (LMIs) is formulated to assess global asymptotic stability of discrete-time delayed systems. Moreover, Abel’s lemma is employed to further reduce conservatism in the stability analysis of switched systems compared to previous studies. Unlike its continuous-time counterpart, the discrete-time model exhibits higher complexity due to the interactions among subsystems induced by switching. To demonstrate the effectiveness of the proposed method, simulation results are provided for two numerical examples.