Non‐Monotonic Based Event‐Triggered Control of Switching Time‐Delay Systems With Robust Stability Under Parametric Uncertainty

This paper presents a novel and efficient approach based on Non‐Monotonic Lyapunov–Krasovskii Functional (NMLKF) for the stability analysis and stabilization of discrete‐time switching systems with time delay. A state‐feedback controller with input delay is synthesized and integrated with an Event‐Triggered Control (ETC) scheme. According to previous research, for the first time within the NMLKF framework and for the specific class of discrete‐time switched linear systems with constant input delay, the ETC mechanism is incorporated and analyzed. This integration reduces the need for continuous updates at every time step and results in resource savings. In the first stage of analyzing switching systems with time delay, system stability is examined over an ‐step horizon, without being restricted to only a few time steps. Subsequently, appropriate non‐monotonic robust stability conditions are derived for systems with parametric uncertainties. In this approach, the strict requirement of monotonic decrease of the Lyapunov functional is replaced with non‐monotonic conditions, providing greater flexibility in selecting Lyapunov–Krasovskii functionals. Within the NMLKF framework, a set of sufficient conditions expressed as Linear Matrix Inequalities (LMIs) is proposed to assess the overall long‐term stability of systems with delay systems. The performance of the proposed method is illustrated through simulation results on five numerical examples.