Further refinements in stability conditions for time-varying delay systems

Improved Stability Criteria for Delayed Neural Networks Using a Quadratic Function Negative-Definiteness Approach

“…Inspired by Chen et al [25], Oliveira and Souza [26], and Zhang et al [27], we construct a novel L-K functional candidate as…”

“…As stated in [36], it is less conservative than the one in [12]. Although an LMI-based necessary and sufficient condition is recently presented in [26], the involved LMIs are of much higher calculation complexity. On the one hand, p 2 NVs are introduced, and on the other hand, the dimensions of the obtained LMIs are 2 p, which is double as those in Lemma 3.…”

“…, it is necessary to get the exact explicit expressions of the matrices j ( j = 0, 1, 2). However, it seems that the proposed methods in [25], [26], and [27] are tedious to work them out since a large number of algebraic manipulations by hand are required. The following result paves a simple way to derive i from the expression of M(h t ).…”

“…Later, the N-dependent quadratic functional is extended in a new L-K functional [25], where three N-dependent quadratic functionals are constructed. Recently, when dealing with linear systems with time-varying delays, instead of the double-integral term t t−h M t sẋ T (u)Rẋ(u)duds, two integral terms, i.e., [26], where h(t) is a timevarying function belonging to a closed interval [0, h M ], and x(•) is the neural state. The two different matrices R 1 and R 2 provide more freedom to relax the resulting stability condition, which is verified in [27].…”

“…is recently developed by introducing two slack matrices [26], and soon after, it is extended to general cases [27]. It should be mentioned that, when the above methods are applied, it is tedious to calculate the matrix coefficients j ( j = 0, 1, 2).…”