Improved Lyapunov Stability Criteria of Delay Systems and Application to Uncertain Complex Networks: New Uncertainty Estimation Method

This paper addresses theoretical limitations in Lyapunov-Krasovskii methods for time-varying delay systems through three principal contributions. First, a novel delay-dependent inequality for the derivatives of the Lyapunov function is proposed, which fundamentally distinguishes our approach from classical Halanay-type inequalities through explicit time-varying parameterization. An enhanced prescribed-time stability theorem for Filippov systems with time-varying delays and uncertainties is established by employing variable substitution and constant variation techniques. This effectively avoids the misuse of the comparison principle. Second, two innovative event-triggered intermittent control (ET-IC) strategies are introduced. These strategies incorporate hybrid intermittent logic to ensure that triggers occur exclusively during control intervals while maintaining system stability during rest intervals. Third, considering the non-eliminability of uncertainties in time-varying delay systems, adaptive mechanism is adopted based on a novel uncertainty estimation method. This method eliminates singularity issues when the estimation errors of uncertainties approach zero. These contributions lead to significant theoretical advances, including the rigorous exclusion of Zeno behavior through guarantees of minimum inter-event times and the prescribed-time stabilization of uncertain complex networks with time-varying delays within a unified framework that addresses both uncertainties and switching topologies. Finally, numerical simulations of a network consisting of two Lorenz systems are given to illustrate the correctness of the main results.