Delay-dependent Robust Stability Research Articles

An improved robust stability analysis for systems with two delays by extracting overlapping feature

In this paper, a delay-dependent robust stability criterion is proposed for linear systems with two delays. For delay-dependent stable systems, the delays are very small in nature. So, they may overlap each other. This overlapping information may be exploited to obtain a less conservative criterion. To extract such information, a special type of simple Lyapunov–Krasovskii functional is considered. To derive the criterion in form of Linear Matrix inequalities, a matrix variable approach is used. Some numerical examples are presented to validate the less conservativeness of the proposed criterion.

Improved Results on Delay-Dependent Stability of LFC Systems with Multiple Time-Delays

In this paper, the problem of delay-dependent robust stability of uncertain load frequency control (LFC) systems with multiple time-delays and exogenous power system disturbance has been considered. Using Lyapunov–Krasosvskii functional method, less conservative delay-dependent stability criteria are proposed in linear matrix inequality formulation to compute the maximum value of the time-delays within which the LFC system under consideration remains asymptotically stable in the sense of Lyapunov. Compared to the existing result in the literature, the proposed result takes into account the effect of unknown exogenous load disturbance into the stability analysis, imparting more applicability and usefulness to the resulting stability criterion in real-time conditions.

New delay-dependent robust exponential stability for uncertain stochastic systems with multiple delays based on extended reciprocally convex approach

New delay-dependent robust exponential stability for uncertain stochastic systems with multiple delays based on extended reciprocally convex approach

Stochastic sampled data robust stabilisation of T-S fuzzy neutral systems with randomly occurring uncertainties and time-varying delays

This paper is concerned with the stochastic sampled data robust stabilisation of T-S fuzzy neutral systems with randomly occurring uncertainties and time-varying delays. The sampling period is assumed to be m in number, whose occurrence probabilities are given constants and satisfy Bernoulli distribution. By introducing an improved Lyapunov–Krasovskii functional with new triple integral terms and by combining both the convex combination technique and reciprocal convex technique, delay-dependent robust stability criteria are obtained in terms of linear matrix inequalities. These linear matrix inequalities can be easily solved by using standard convex optimisation algorithms. The designed stochastic sampled data fuzzy controller gain can be obtained. Finally, three numerical examples are given to illustrate the effectiveness of the proposed methods.

Further improvement on delay-dependent robust stability criteria for neutral-type recurrent neural networks with time-varying delays

This paper is concerned with the problem of improved delay-dependent robust stability criteria for neutral-type recurrent neural networks (NRNNs) with time-varying delays. Combining the Lyapunov–Krasovskii functional with linear matrix inequality (LMI) techniques and integral inequality approach (IIA), delay-dependent robust stability conditions for RNNs with time-varying delay, expressed in terms of quadratic forms of state and LMI, are derived. The proposed methods contain the least number of computed variables while maintaining the effectiveness of the robust stability conditions. Both theoretical and numerical comparisons have been provided to show the effectiveness and efficiency of the present method. Numerical examples are included to show that the proposed method is effective and can provide less conservative results.

On improved delay-dependent robust stability criteria for uncertain systems with interval time-varying delay

This paper considers the problem of delay-dependent robust stability for uncertain systems with interval time-varying delays. By using the direct Lyapunov method, a new Lyapunov-Krasovskii (L-K) functional is introduced based on decomposition approach, when dealing with the time derivative of L-K functional, a new tight integral inequality is adopted for bounding the cross terms. Then, a new less conservative delay-dependent stability criterion is formulated in terms of linear matrix inequalities (LMIs), which can be easily solved by optimization algorithms. Numerical examples are given to show the effectiveness and the benefits of the proposed method.

Robust Delay-Dependent Stability Criteria for Time-Varying Delayed Lur’e Systems of Neutral Type

This paper deals with the problem of the robust delay-dependent stability of uncertain Lur'e systems with neutral-type time-varying delays. By constructing a set of Lyapunov---Krasovskii functional, less conservative robust stability criteria are derived in terms of linear matrix inequalities. The contribution in reduced conservation of the proposed stability criteria relies on the reciprocally convex method and Wirtinger inequality, which provides tighter upper bound than Jensen inequality. Three numerical examples are provided to show the effectiveness of the proposed method.

Improved Delay-dependent Robust Stability Analysis for Neutral-type Uncertain Neural Networks with Markovian jumping Parameters and Time-varying Delays

Abstract This paper deals with the problem of robust stochastic stability analysis for a class of neutral-type uncertain neural networks with Markovian jumping parameters and time-varying delays. By introducing an novel mode-dependent Augmented Lyapunov-Krasovskii functional with delay partitioning and Wirtinger-based integral inequality techniques, some improved delay-dependent stochastically stable conditions are proposed in the form of LMIs. Numerical simulations are provided to show the effectiveness and less conservatism of the results.

Delay-dependent robust stability criteria for stochastic neural networks of neutral-type with interval time-varying delay and linear fractional uncertainties

In this paper, we investigate the problem of robust stability for a class of delayed neural networks of neutral-type with linear fractional uncertainties. The activation functions are assumed to be unbounded, non-monotonic and non-differentiable, and the delay is assumed to be time-varying and belonging to a given interval, which means that the lower and upper bounds of the interval time-varying delay are available. By constructing a general form of the Lyapunov–Krasovskii functional, and using the linear matrix inequality (LMI) approach, we derive several delay-dependent stability criteria in terms of LMI. Finally, we give a number of examples to illustrate the effectiveness of the proposed method.

Delay-dependent stability of neutral system with mixed time-varying delays and nonlinear perturbations using delay-dividing approach.

This paper studies delay-dependent robust stability problem for neutral system with mixed time-varying delays and nonlinear perturbations. Based on the delay-dividing approach, a novel Lyapunov functional is constructed, and a novel delay-dependent stability criterion is derived to guarantee the robust stability of the neutral system. Expressed in terms of linear matrix inequalities, the stability condition can be checked using the numerically efficient Matlab LMI Control Toolbox. Two numerical examples are provided to demonstrate the effectiveness and the reduced conservatism of the analysis result.

Improved criteria on robust stability and [formula omitted] performance for linear systems with interval time-varying delays via new triple integral functionals

This paper analyzes delay-dependent robust stability and H∞ performance of linear systems with an interval time-varying delay, based on a new Lyapunov–Krasovskii functional containing new triple integral terms. The time derivative of the Lyapunov–Krasovskii functional produces not only the strictly proper rational functions but also the non-strictly proper rational functions of the time-varying delays with first-order denominators. The combinations of the rational functions are directly handled via the Jensen inequality lemma and the lower bound lemma for reciprocal convexity, whereas such combinations were approximated in the literature. The proposed criteria become less conservative with the significantly smaller number of decision variables than the existing criteria, which will be demonstrated by some numerical examples.

Stabilization of Fuzzy Markovian Jumping Systems with Distributed Delay

This paper is concerned with the stabilization problem for fuzzy Markovian jumping systems with distributed time delay. First, fuzzy Markovian jumping systems with distributed time delay are peoposed. Second, a novel criterion of delay-dependent robust stabilization for fuzzy Markovian jumping systems is established in terms of linear matrix inequalities (LMIs) by using Lyapunov stability theory and free-weighting matrix method. When these LMIS are feasible, an explicit expression of a desired adjustable state feedback controller is given. Based on the obtained criterion, the introduced controller ensures the overall closed-loop system asymptotically stable in mean square sense for all admissible uncertainties and time delay.

Delay-dependent robust stability and stabilization of uncertain memristive delay neural networks

In this paper, a general class of uncertain memristive neural networks with time-delay is formulated and studied. And the problems of robust stability analysis and robust controller designing of the new model are derived. The uncertainty is assumed to be norm-bound and appears in all the matrices of the state-space model. There are few studies concerned the robust analysis of the memristive neural networks, so these conditions are improvements and extensions of the existing results in the literature. The proposed methods are dependent on the size of the delay and are given in terms of linear matrix inequalities. Finally, the validity of the theoretical results are demonstrated via some numerical examples.

Delay-dependent robust stability analysis for switched time-delay systems with polytopic uncertainties

Summary In this paper, sufficient conditions are provided for the stability of switched retarded and neutral time-delay systems with polytopic-type uncertainties. It is assumed that the delay in the system dynamics is time-varying and bounded. Parameter-dependent Lyapunov functionals are employed to obtain criteria for the exponential stability of the system in the form of linear matrix inequality (LMI). Free-weighting matrices are then provided to express the relationship between the system variables and the terms in the Leibniz–Newton formula. Numerical examples are presented to show the effectiveness of the results. Copyright © 2014 John Wiley & Sons, Ltd.

Delay-decomposing approach to robust stability for switched interval networks with state-dependent switching.

This paper is concerned with a class of nonlinear uncertain switched networks with discrete time-varying delays . Based on the strictly complete property of the matrices system and the delay-decomposing approach, exploiting a new Lyapunov-Krasovskii functional decomposing the delays in integral terms, the switching rule depending on the state of the network is designed. Moreover, by piecewise delay method, discussing the Lyapunov functional in every different subintervals, some new delay-dependent robust stability criteria are derived in terms of linear matrix inequalities, which lead to much less conservative results than those in the existing references and improve previous results. Finally, an illustrative example is given to demonstrate the validity of the theoretical results.

Improved Delay-Dependent Robust Stability Criteria for a Class of Uncertain Neutral Type Lur’e Systems with Discrete and Distributed Delays

This paper is concerned with the problem of delay-dependent robust stability analysis for a class of uncertain neutral type Lur’e systems with mixed time-varying delays. The system has not only time-varying uncertainties and sector-bounded nonlinearity, but also discrete and distributed delays, which has never been discussed in the previous literature. Firstly, by employing one effective mathematical technique, some less conservative delay-dependent stability results are established without employing the bounding technique and the mode transformation approach. Secondly, by constructing an appropriate new type of Lyapunov-Krasovskii functional with triple terms, improved delay-dependent stability criteria in terms of linear matrix inequalities (LMIs) derived in this paper are much brief and valid. Furthermore, both nonlinearities located in finite sector and infinite one have been also fully taken into account. Finally, three numerical examples are presented to illustrate lesser conservatism and the advantage of the proposed main results.

Improved Results on Robust Stability for Systems with Interval Time-Varying Delays and Nonlinear Perturbations

This paper investigated delay-dependent robust stability criteria for systems with interval time-varying delays and nonlinear perturbations. A delay-partitioning approach is used in this paper, the delay-interval is partitioned into multiple equidistant subintervals, a new Lyapunov-Krasovskii (L-K) functional contains some triple-integral terms, and augment terms are introduced on these intervals. Then, by using integral inequalities method together with free-weighting matrix approach, a new less conservative delay-dependent stability criterion is formulated in terms of linear matrix inequalities (LMIs), which can be easily solved by optimization algorithms. Numerical examples are given to show the effectiveness and the benefits of the proposed method.

Novel Stabilization Conditions for Uncertain Singular Systems with Time-Varying Delay

The problem of delay-dependent robust stabilization for continuously singular time-varying delay systems with norm-bounded uncertainties is investigated in this paper. First, based on some mathematical transform, the uncertain singular system is described in a form which involves the time-delay integral items. Then, in terms of the delay-range-dependent Lyapunov functional and the LMI technique, the improved delay-dependent LMIs-based conditions are established for the uncertain singular systems with time-varying delay to be regular, causal, and stable. Furthermore, by solving these LMIs, an explicit expression for the desired state feedback control law can be obtained; thus, the regularity, causality, and stability of the closed-loop system are guaranteed. In the end, numerical examples are given to illustrate the effectiveness of the proposed methods.

New Results on Delay-dependent Robust Stability of Interval State-Delayed Linear Systems with Nonlinear Perturbations

In this paper, we consider the problem of delay-dependent stability of a class of continuous-time and discrete-time linear systems with nonlinear perturbations and time-varying state-delays using Lyapunov functional approach. By exploiting candidate Lyapunov functionals, less conservative new robust stability criteria (sufficient conditions) are derived for computing the maximum allowable bound of the delay-range, within which, the uncertain systems under consideration remain asymptotically stable in the sense of Lyapunov. The proposed criteria are derived using reciprocal convex approach, and they are expressed as a set of solvable LMI conditions. The effectiveness of the proposed criteria are validated using standard numerical examples.

Robust Stability of Neutral System with Mixed Time-Varying Delays and Nonlinear Perturbations Using Delay Decomposition Approach

This paper investigates the robust delay-dependent stability problem for neutral system with mixed delays and nonlinear perturbations. A delay decomposition approach is used in this paper in which the information of the delayed plant states can be taken into full consideration. Then, based on a special Lyapunov functional approach, the novel delay-dependent stability criteria are obtained in terms of linear matrix inequalities (LMIs). A numerical example illustrates the effectiveness of the derived method and the improvement over some existing methods.