Delay-dependent stability criteria for systems with asymmetric bounds on delay derivative

This paper discretizes the states, a method introduced in [18] for constant delayed systems, not only in constructing the Lyapunov–Krasovskii (L–K) functional but also in designing the integral inequality technique [17,19] for time-varying delayed systems, which increase the order of uncorrelated augmentation [5,21,22]. Based on the discretized state, [10,27]ʹs piecewise analysis method is applied to confirm the system stability in whole delay bound. Asymmetric variation of the delay derivative is assumed so that direct extension to all constraints of the delay derivative can be achieved. Examples show the resulting criteria improve the allowable delay bounds over all existing ones in the literature.