Shahid Beheshti University International Journal of Research and Technology in Electrical Industry 2821-0190 4 2 2025 07 01 Robust Stability Analysis of Switching Time-Delay Systems via a Novel Non-Monotonic Lyapunov–Krasovskii Approach 553 564 106456 10.48308/ijrtei.2025.241244.1100 EN Saeed Ahmadi Bu-Ali Sina University, Shahid Mostafa Ahmadi Roshan Street, Hamedan Younes Solgi Bu-Ali Sina University, Shahid Mostafa Ahmadi Roshan Street, Hamedan Journal Article 2025 08 24 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. https://ijrtei.sbu.ac.ir/article_106456_6351bbef6bc6919b4989192565881c40.pdf