Enhanced Exponential Stability Analysis for Switched Linear Time-Varying Delay Systems Under Admissible Edge-Dependent Average Dwell-Time Strategy
通过构造新的增广Lyapunov-Krasovskii泛函并利用Bessel-Legendre积分不等式，给出了切换时变时滞系统在容许边依赖平均驻留时间策略下的指数稳定性条件，数值和实际例子验证了方法的优越性。
This article focuses on the exponential stability analysis for the switched linear systems with time-varying delay. By constructing a new augmented multiple Lyapunov–Krasovskii functional, containing time-varying delay information, coupling of current and delayed states, state integral, and state derivative terms the feasibility of the stability condition is considerably enhanced. Besides, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> -order canonical Bessel–Legendre integral inequality and the convex function property are utilized to give more relaxed criteria. On the other hand, for the first time, more flexible switching is employed with an admissible edge-dependent average dwell-time strategy for the switched time-varying delay systems (STDSs). Novel improved delay-dependent stability conditions are expressed by two theorems in the form of linear matrix inequalities which can be used to guarantee the exponential stability of the STDSs in the different delay conditions. Finally, significant improvements over the state-of-the-art in terms of delay upper bound, exponential decay rate, and dwell time are presented by simulating two numerical examples and one practical example including streams water quality preserving.