Event-triggered uniform ultimate boundedness control for singular systems with time-varying delays via an improved Halanay technique

This paper studies event-triggered uniform ultimate boundedness control for singular linear systems with time-varying delays. A nonperiodic event-triggered mechanism with an exponentially decaying threshold and a positive absolute threshold is introduced to reduce redundant transmissions and exclude Zeno behavior. By treating the triggering-induced measurement error as a bounded perturbation, the closed-loop system is transformed into a singular delay system. A Halanay-type estimation technique is incorporated into the analysis to derive sufficient conditions guaranteeing admissibility and uniform ultimate boundedness of the closed-loop system. In contrast to conventional Lyapunov–Krasovskii functional approaches, the proposed method avoids augmented functionals with multiple integral terms and numerous auxiliary variables, resulting in computationally efficient LMI-based design conditions. These conditions provide a tractable co-design method for the controller and triggering parameters, while characterizing the effects of the delay bound, decay rate, thresholds, and ultimate bound. Finally, a numerical example, an electrical circuit application, and a comparative example with an existing LKF-based method are provided to verify the theoretical results and demonstrate the practical applicability and computational advantages of the proposed approach.