In this paper, we investigate the problem of delay-range-dependent robust stability analysis for uncertain neutral systems with interval time-varying delays and nonlinear perturbations. The restriction on the derivative of the discrete interval time-varying delay is removed. By applying the augmented Lyapunov–Krasovskii functional approach, new improved integral inequalities, descriptor model transformation, Leibniz–Newton formula and utilization of zero equation, new delay-range-dependent robust stability criteria are derived in terms of linear matrix inequalities (LMIs) for the considered systems. Numerical examples have shown to illustrate the significant improvement on the conservatism of the delay upper bound over some reported results.
This paper deals with the problem of delay-range-dependent robust passivity analysis of uncertain neutral-type neural networks with distributed interval time-varying delay under the effects of leakage delay. The uncertainties under consideration are norm-bounded uncertainties and the restriction on the derivative of the discrete and distributed interval time-varying delays is removed, which means that a fast interval time-varying delay is allowed. By applying a novel Lyapunov-Krasovskii functional approach, improved integral inequalities, Leibniz-Newton formula and utilization of zero equation, then a new delay-rangedependent passivity criterion of neutral-type neural networks with distributed interval time-varying delay under the effects of leakage delay is established in terms of linear matrix inequalities (LMIs). Furthermore, some less conservative delay-dependent passivity criteria are obtained. Moreover, we derived a robust passivity criterion for uncertain neutral-type neural networks with distributed interval time-varying delay under the effects of leakage delay. Besides, a less conservative delay-dependent robust passivity criterion is obtained. Finally, five numerical examples are given to show the effectiveness and less conservativeness of the proposed methods.
This paper deals with the problems of delay-dependent stability and H∞ performance for uncertain neutral systems with time-varying delays, and nonlinear perturbations. The time-varying delays are neutral, discrete, and distributed time-varying delays that the upper bounds for the delays are available. The restrictions on the derivatives of the discrete and distributed time-varying delays are removed, which mean that a fast discrete time-varying delay is allowed. The uncertainties under consideration are nonlinear time-varying parameter perturbations and norm-bounded uncertainties, respectively. Firstly, by applying a novel Lyapunov-Krasovskii functional approach, Wirtinger-based integral inequality, Peng-Park’s integral inequality, decomposition technique of constant matrix, descriptor model transformation, Leibniz Newton formula and utilization of zero equation, and improved delay-dependent bounded real lemmas (BRL) for systems are established in terms of linear matrix inequalities (LMIs). Then, based on the obtained BRL, some less conservative delay-dependent stability criteria of uncertain neutral systems with mixed time-varying delays and nonlinear perturbations are obtained and improved H∞ performance criterion with the framework of LMIs is introduced. Finally, some numerical examples are given to illustrate that the presented method is effective.
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