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.     

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.     

Novel global stability criteria for high-order Hopfield-type neural networks with time-varying delays

This paper discusses a generalized model of high-order Hopfield-type neural networks with time-varying delays. Some novel global stability criteria of the system is derived by using Lyapunov method, linear matrix inequality (LMI) and analytic technique. The LMI-based criteria obtained here are computationally more flexible and more generic than many other existing criteria. A numerical example is given to illustrate our result.     

Robust stability criteria for a class of uncertain discrete-time systems with time-varying delay

In this paper, we consider the problem of delay-dependent robust stability of a class of uncertain discrete-time systems with time-varying delay using Lyapunov functional approach. Two categories of time-varying uncertainties are considered for the robust stability analysis: viz., (i) nonlinear perturbations and (ii) norm-bounded uncertainties. In the proposed stability analysis, by exploiting a candidate Lyapunov functional, and using minimal number of slack matrix variables, less conservative stability criteria are developed in terms of linear matrix inequalities (LMIs) for computing the maximum allowable bound of the delay-range, within which, the uncertain system under consideration remains asymptotically stable in the sense of Lyapunov. The effectiveness of the proposed stability criteria is demonstrated using standard numerical examples.     

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.     

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.     

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.     

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.     

Uniform stability for thermoelastic systems with boundary time-varying delay

In this paper we consider a thermoelastic system with boundary time-varying delay. Using the energy method, we show, under suitable assumptions, that the damping effect through heat conduction is still strong enough to uniformly stabilize the system even in the presence of boundary time-varying delay. Our result improves earlier results existing in the literature.     

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.     

Stability analysis for stochastic jump systems with time-varying delay

This paper deals with the mean-square asymptotic stability of stochastic Markovian jump systems with time-varying delay. Based on a new stochastic inequality and convex analysis property, some novel stability conditions are presented. In the derivation, the information of the time-varying delay is retained and the estimation of it by the worst-case enlargement is not involved. Some special cases of the systems under consideration are also investigated. Illustrative examples are given to show the effectiveness of the proposed approach.     

Stability of linear systems with time-varying delays: A direct frequency domain approach

The stability of linear systems with uncertain bounded time-varying delays (without any constraints on the delay derivatives) is analyzed. It is assumed that the system is stable for some known constant values of the delays (but may be unstable for zero delay values). The existing (Lyapunov-based) stability methods are restricted to the case of a single non-zero constant delay value, and lead to complicated and restrictive results. In the present note for the first time a stability criterion is derived in the general multiple delay case without any constraints on the delay derivative. The simple sufficient stability condition is given in terms of the system matrices and the lengths of the delay segments. Different from the existing frequency domain methods which usually apply the small gain theorem, the suggested approach is based on the direct application of the Laplace transform to the transformed system and on the bounding technique in _L2$L_2$. A numerical example illustrates the efficiency of the method.     

Observer-based robust control for uncertain systems with time-varying delay

This paper is concerned with the function observer-based stabilizationfor time-varying delay systems with parameter uncertainties.The uncertain systems tackled in this paper involve uncertaintyin quadratic constrained form which includes the well-knownnorm-bounded time-varying uncertainty as a special case. Interms of Razumikhin-type stability theorem, we show that thefeasibility of several matrix inequalities guarantees the solvabilityof the addressed problem. Furthermore, we propose a parametricapproach for function observer-based robust stabilizer design.     

Stabilization of nonlinear networked systems with sensor random packet dropout and time-varying delay

In this paper, a nonlinear stochastic system model is proposed to describe the networked control systems (NCSs) with both random packet dropout and network-induced time-varying delay. Based on this more general nonlinear NCSs model, by choosing appropriate Lyapunov functional and employing new discrete Jensen type inequality, a sufficient condition is derived to establish the quantitative relation of maximum allowable delay upper bound, packet dropout rate and the nonlinear level to the exponential stability of the nonlinear NCSs. Design procedures for output feedback controller are also presented in terms of utilizing cone complementarities linearization algorithm or solving corresponding linear matrix inequalities (LMIs). Illustrative examples are provided to demonstrate the effectiveness of the proposed method.     

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

This paper proposes an approach for the robust stability of uncertain systems with interval time-varying delay. The key features of the approach include the introduction of uncorrelated augmented matrix items into the Lyapunov functional and the use of a tighter bounding technology. Unlike existing methodologies, the proposed approach involves neither free weighting matrices nor any model transformation. It can, however, lead to much less conservative stability criteria than the existing ones for the systems under consideration. Numerical examples show that the proposed criteria improve the existing results significantly with much less computational effort.     

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 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.     

Improved stability criteria for time-varying delayed T-S fuzzy systems via delay partitioning approach

This paper focuses on the stability analysis for uncertain Takagi-Sugeno (T-S) fuzzy systems with interval time-varying delay. The uncertainties of system parameter matrices are assumed to be time-varying and norm-bounded. Some new Lyapunov-Krasovskii functionals (LKFs) are constructed by nonuniformly dividing the whole delay interval into multiple segments and choosing different Lyapunov functionals to different segments in the LKFs. By employing these LKFs, some new delay-derivative-dependent stability criteria are established for the nominal and uncertain T-S fuzzy systems in a convex way. These stability criteria are derived that depend on both the upper and lower bounds of the time derivative of the delay. By employing the new delay partitioning approach, the obtained stability criteria are stated in terms of linear matrix inequality (LMI). They are equivalent or less conservative while involving less decision variables than the existing results. Finally, numerical examples are given to illustrate the effectiveness and reduced conservatism of the proposed results.     

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.