Augmented zero equality approach to stability for linear systems with time-varying delay

This work focuses the delay-dependent stability problem for linear systems with time-varying delays. By composing a suitable augmented Lyapunov–Krasovskii functionals, using recent developed integral inequality and choosing newly states, a set of sufficient conditions for stability condition is induced within framework of linear matrix inequalities (LMIs). To enhance the feasible region of stability, single augmented zero equality is established with the augmented state vectors for the first time and the equality constraint is incorporated into a simple stability criterion by utilizing Finsler's lemma. The comparison of maximum bounds of time-delay with various results proposed by recent studies will be conducted in numerical examples to demonstrate the superiority of the theorems presented by this paper.