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.     

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.     

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.     

Synchronization stability of general complex dynamical networks with time-varying delays: A piecewise analysis method

The synchronization problem of some general complex dynamical networks with time-varying delays is investigated. Both time-varying delays in the network couplings and time-varying delays in the dynamical nodes are considered. The delays considered in this paper are assumed to vary in an interval, where the lower and upper bounds are known. Based on a piecewise analysis method, the variation interval of the time delay is firstly divided into several subintervals, by checking the variation of the derivative of a Lyapunov function in every subinterval, then the convexity of matrix function method and the free weighting matrix method are fully used in this paper. Some new delay-dependent synchronization stability criteria are derived in the form of linear matrix inequalities. Two numerical examples show that our method can lead to much less conservative results than those in the existing references.     

Observer-based fault detection for networked discrete-time infinite-distributed delay systems with packet dropouts

This paper addresses the problem of fault detection for networked discrete-time infinite-distributed delay systems with packet dropouts. Both sensor-to-controller and controller-to-actuator packet dropouts are described by two different Bernoulli distributed white sequences, respectively. The problem addressed is to design an observer-based fault detection filter (FDF) such that the error between the residual and the fault is made as small as possible. Unlike most of the existing literature, we have noted that the control input of the observer is different from that of the plant because of packet dropouts in the controller-to-actuator link. Sufficient condition for the existence of the FDF is derived in terms of some linear matrix inequalities (LMIs). When these LMIs are feasible, the explicit expression of the desired FDF can also be characterized. A numerical example is exploited to show the effectiveness of the obtained results.     

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 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.     

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.     

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.     

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.     

Delay-dependent stability of neutral systems with time-varying delays using delay-decomposition approach

This paper is concerned with the problem of asymptotic stability of neutral systems. A new delay-dependent stability condition is derived in terms of linear matrix inequality to ensure a large upper bound of the time-delay by non-uniformly dividing the delay interval into multiple segments. A new Lyapunov-Krasovskii functional is constructed with different weighting matrices corresponding to different segments in the Lyapunov-Krasovskii functional, where both constant time delays and time-varying delays have been taken into account. Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.     

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 results on the stability analysis of linear neutral systems with delay decay approach

In this paper, the investigation of the asymptotical stability of linear neutral systems with time-varying delay has been presented. In order to achieve the desired results, the integral inequality approach was used to express relationships between terms of Newton-Leibniz formula technique and was constructed an appropriate Lyapunov-Krasovskii functional. By improving a delay decay approach, the stability criteria for the zero solution of system were formulated as linear matrix inequalities (LMIs) which can be easily solved. Two numerical examples have been given to show the applicability of established assumptions and the effectiveness of proposed method by MATLAB-Simulink.     

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.     

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.     

Synchronization of non-autonomous chaotic systems with time-varying delay via delayed feedback control

In this paper, we investigate the synchronization of non-autonomous chaotic systems with time-varying delay via delayed feedback control. Using a combination of Riccati differential equation approach, Lyapunov-Krasovskii functional, inequality techniques, some sufficient conditions for exponentially stability of the error system are formulated in form of a solution to the standard Riccati differential equation. The designed controller ensures that the synchronization of non-autonomous chaotic systems are proposed via delayed feedback control and intermittent linear state delayed feedback control. Numerical simulations are presented to illustrate the effectiveness of these synchronization criteria.     

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.     

Delay dependent stability analysis of neutral systems with mixed time-varying delays and nonlinear perturbations

This paper is concerned with the problem of stability of neutral systems with interval time-varying delays and nonlinear perturbations. The uncertainties under consideration are nonlinear time-varying parameter perturbations and norm-bounded uncertainties. A new delay-dependent stability condition is derived in terms of linear matrix inequality by constructing a new Lyapunov functional and using some integral inequalities without introducing any free-weighting matrices. Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.