Improved delay-dependent robust stability criteria for uncertain time delay systems

This paper deals with the robust stability analysis for uncertain systems with time-varying delay. New delay-dependent robust stability criteria of uncertain time-delay systems are proposed by exploiting appropriate Lyapunov functional candidate. These developed results have advantages over some previous ones in that they have fewer matrix variables yet less conservatism, due to the introduction of a method to estimate the upper bound of the derivative of Lyapunov functional candidate without ignoring the additional useful terms. Numerical examples are given to demonstrate the effectiveness and the advantage of the proposed method.     

Improved delay-dependent stability criterion for neural networks with time-varying delay

In this paper, the problem of delay-dependent asymptotic stability criterion for neural networks with time-varying delay has been considered. A new class of Lyapunov functional which contains a triple-integral term is constructed to derive some new delay-dependent stability criteria. The obtained criteria are less conservative because free-weighting matrices method and a convex optimization approach are considered. Finally, numerical examples are given to illustrate the effectiveness of the proposed method.     

Robust stability analysis of uncertain systems with two additive time-varying delay components

This paper is concerned with stability analysis for uncertain systems. The systems are based on a new time-delay model proposed recently, which contains multiple successive delay components in the state. The relationship between the time-varying delay and its upper bound is taken into account when estimating the upper bound of the derivative of Lyapunov functional. As a result, some less conservative stability criteria are established for systems with two successive delay components and parameter uncertainties. Numerical examples show that the proposed criteria are effective and are an improvement over some existing results in the literature.     

Absolute stability criteria for a class of nonlinear singular systems with time delay

This paper deals with the problem of absolute stability for a class of time-delay singular systems with sector-bounded nonlinearity. Both delay-independent and delay-dependent criteria are presented and formulated in the form of linear matrix inequalities (LMIs). Neither model transformation nor a bounding technique for cross-terms, nor a slack variable method is involved in obtaining the stability criteria. Numerical examples are given to show the effectiveness and improvements over some existing results.     

A new augmented Lyapunov-Krasovskii functional approach for stability of linear systems with time-varying delays

This paper proposes improved delay-dependent conditions for asymptotic stability of linear systems with time-varying delays. The proposed method employs a suitable Lyapunov-Krasovskii’s functional for new augmented system. Based on Lyapunov method, delay-dependent stability criteria for the systems are established in terms of linear matrix inequalities (LMIs) which can be easily solved by various optimization algorithms. Three numerical examples are included to show that the proposed method is effective and can provide less conservative results.     

Novel robust stability criteria for uncertain systems with time-varying delay

This paper is concerned with the delay-dependent stability and robust stability criteria for linear systems with time-varying delay and norm-bounded uncertainties. Through constructing a general form of Lyapunov–Krasovskii functional, and using integral inequalities, some slack matrices and newly established convex combination condition in the calculation, the delay-dependent stability criteria are derived in terms of linear matrix inequalities. Numerical examples are given to illustrate the improvement on the conservatism of the delay bound over some reported results in the literature.     

Improved delay-dependent stability criteria for continuous system with two additive time-varying delay components

This paper investigated the problem of improved delay-dependent stability criteria for continuous system with two additive time-varying delay components. Free weighting matrices and convex combination method are not involved, which achieves much less numbers of linear matrix inequalities (LMIs) and LMIs scalar decision variables. By taking advantage of integral inequality and new Lyapunov–Krasovskii functional, new less conservative delay-dependent stability criterion is derived. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.     

Robust exponential stability and stabilizability of linear parameter dependent systems with delays

The robust exponential stability and stabilizability problems are addressed in this paper for a class of linear parameter dependent systems with interval time-varying and constant delays. In this paper, restrictions on the derivative of the time-varying delay is not required which allows the time-delay to be a fast time-varying function. Based on the Lyapunov-Krasovskii theory, we derive delay-dependent exponential stability and stabilizability conditions in terms of linear matrix inequalities (LMIs) which can be solved by various available algorithms. Numerical examples are given to illustrate the effectiveness of our theoretical results.     

LMI-based criteria for stability of high-order neural networks with time-varying delay

This paper investigates the stability of a class of high-order neural networks with time-varying delay, which can be considered as an expansion of Hopfield neural networks and is seldom considered in the literature. Based on the Lyapunov stability theory and linear matrix inequality (LMI) technique, sufficient conditions guaranteeing the global exponential stability of the equilibrium point are presented. Two examples are given to show the effectiveness of the proposed conditions. The obtained results are also shown to be different from and more general than existing ones.     

On robustly exponential stability of uncertain neutral systems with time-varying delays and nonlinear perturbations

The issue of robustly exponential stability for uncertain neutral-type systems is considered in this paper. The uncertainties are nonlinear and the delays are time-varying. In terms of a linear matrix inequality (LMI), the new sufficient stability condition with delay dependence is presented. The model transformation and bounding techniques for cross terms are avoided based on an integral inequality. Two illustrative examples are proposed to show the effectiveness of our method.     

Improved results on robust exponential stability criteria for neutral-type delayed neural networks

In this paper, we investigate the problem of robust global exponential stability analysis for a class of neutral-type neural networks. The interval time-varying delays allow for both slow and fast time-varying delays. The values of the time-varying uncertain parameters are assumed to be bounded within given compact sets. Improved global exponential stability condition is derived by employing new Lyapunov-Krasovskii functional and the integral inequality. The developed nominal and robust stability criteria is delay-dependent and characterized by linear-matrix inequalities (LMIs). The developed results are less conservative than previous published ones in the literature, which are illustrated by representative numerical examples.     

Improved stability analysis on delayed neural networks with linear fractional uncertainties

The paper is concerned with robust stability for generalized neural networks (GNNs) with both interval time-varying delay and time-varying distributed delay. Through partitioning the time-delay, choosing one augmented Lyapunov-Krasovskii functional, employing free-weighting matrix method and convex combination, the sufficient conditions are obtained to guarantee the robust stability of the concerned systems. These stability criteria are presented in terms of linear matrix inequalities (LMIs) and can be easily checked. Finally, three numerical examples are given to demonstrate the effectiveness and reduced conservatism of the obtained results.     

Dissipativity analysis for singular systems with time-varying delays

This paper is concerned with the dissipativity analysis problem for singular systems with time-varying delays. A delay-dependent criterion is established to guarantee the dissipativity of the underlying systems using the delay partitioning technique. All the results given in this paper are not only dependent upon the time delay, but also dependent upon the number of delay partitions. The effectiveness and the reduced conservatism of the derived results are demonstrated by two illustrative examples.     

A delay decomposition approach to stability analysis of neutral systems with time-varying delay

This paper presents novel stability criteria for neutral systems with time-varying delay. By developing a delayed decomposition approach, information of the delayed plant states can be taken into full consideration, and new delay-dependent sufficient stability criteria are obtained in terms of linear matrix inequalities (LMIs). Then, based on the Lyapunov method, delay-dependent stability criteria are devised by taking the relationship between terms in the Leibniz-Newton formula into account. Criteria are derived in terms of LMIs, which can be easily solved by using various convex optimization algorithms. Three illustrative numerical examples are given to show less conservatism of our obtained results and the effectiveness of the proposed method.     

Improved results on robust stability of neutral systems with mixed time-varying delays and nonlinear perturbations

This paper considers the problem of robust stability of neutral systems with mixed time-varying delays and nonlinear perturbations. Two type uncertainties such as nonlinear time-varying parameter perturbations and norm-bounded uncertainties have been discussed. Based on the new Lyapunov–Krasovskii functional with triple integral terms, some integral inequalities and convex combination technique, a new delay-dependent stability criterion for the system is established in terms of linear matrix inequalities (LMIs). Finally, four numerical examples are given to illustrate the effectiveness and an improvement over some existing results in the literature with the proposed results.     

New stability criteria for neural networks with time-varying delays

This paper is concerned with the stability analysis problem of neural networks with time delays. The delay intervals [−d(t), 0] and [−h, 0] are divided into m subintervals with equal length. Some free matrices are introduced to build the relationship among the elements of the resultant matrix inequalities. With the above operations, the new stability criteria are built for the general class of neural networks. The conditions are presented in the form of linear matrix inequalities (LMIs), which can be solved by the numerically efficient Matlab LMI toolbox. Several examples are provided to show that our methods are much less conservative than recently reported ones.     

不确定时变时滞退化系统的新鲁棒稳定性判据(英文)

介绍了不确定时变时滞退化系统的一种新的鲁棒稳定性判据,该判据的提出利用适当的Lyapunov-Krasovskii函数方法,由一组线性矩阵不等式表示出来,判据可借助Matlab软件中LMI工具箱中得以验证.最后,数值实例证明了方法的有效性和优势.     

Decentralized stability for switched nonlinear large-scale systems with interval time-varying delays in interconnections

In this paper, the problem of decentralized stability of switched nonlinear large-scale systems with time-varying delays in interconnections is studied. The time delays are assumed to be any continuous functions belonging to a given interval. By constructing a set of new Lyapunov–Krasovskii functionals, which are mainly based on the information of the lower and upper delay bounds, a new delay-dependent sufficient condition for designing switching law of exponential stability is established in terms of linear matrix inequalities (LMIs). The developed method using new inequalities for lower bounding cross terms eliminate the need for overbounding and provide larger values of the admissible delay bound. Numerical examples are given to illustrate the effectiveness of the new theory.     

An improved robust delay-dependent stability criterion for genetic regulatory networks with interval time delays

This paper proposes an improved robust delay-dependent criterion for stability of genetic regulatory networks with delays which vary in an interval. A modified Lyapunov-Krasovskii functional is used to derive a sufficient condition in terms of linear matrix inequalities (LMIs) which can be easily solved by various convex optimization algorithms. The derived stability criterion is less conservative than ones in the literature. A numerical example and simulation results show the effectiveness of the proposed method.