Delay-range-dependent stability for systems with time-varying delay

This paper is concerned with the stability analysis for systems with time-varying delay in a range. An appropriate type of Lyapunov functionals is proposed to investigate the delay-range-dependent stability problem. The present results may improve the existing ones due to a method to estimate the upper bound of the derivative of Lyapunov functional without ignoring some useful terms and the introduction of additional terms into the proposed Lyapunov functional, which take into account the range of delay. Numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method.     

Delay-dependent criteria for robust stability of time-varying delay systems

This paper deals with the problem of delay-dependent robust stability for systems with time-varying structured uncertainties and time-varying delays. Some new delay-dependent stability criteria are devised by taking the relationship between the terms in the Leibniz-Newton formula into account. Since free weighting matrices are used to express this relationship and since appropriate ones are selected by means of linear matrix inequalities, the new criteria are less conservative than existing ones. Numerical examples suggest that the proposed criteria are effective and are an improvement over previous ones.     

Delay-dependent exponential stability analysis for discrete-time switched neural networks with time-varying delay

In this paper, we focus on the stability problem for discrete-time switched neural networks with time-varying delay resorting to the average dwell time method. In terms of linear matrix inequality approach, a delay-dependent sufficient condition of exponential stability is developed for a kind of switching signal with average dwell time. A numerical example is given to show the validness of the established result.     

Delay-dependent robust stabilisation of uncertain discrete-time switched systems with time-varying state delay

This paper considers the stabilisation problem for uncertain discrete-time switched systems with time-varying delay in the state. The uncertainty is assumed to be of structured linear fractional form, which includes the norm-bounded uncertainty as a special case. A stability condition is first proposed by using switched Lyapunov function, which is dependent on the minimum and maximum delay bounds. Based on the result, a switched state feedback controller is designed. Numerical examples are given to illustrate the effectiveness of the result.     

Observer-based robust stabilization for uncertain systems with unknown time-varying delay

This paper focuses on the problem of robust stabilization for a class of linear systems with uncertain parameters and time varying delays in states. The parameter uncertainty is continuous, time varying, and norm-bounded. The state delay is unknown and time varying. The states of the system are not all measurable and an observer is constructed to estimate the states. If a linear matrix inequality (LMI) is solvable, the gains of the controller and observer can be obtained from the solution of the LMI. The observer and controller are dependent on the size of time delay and on the size of delay derivative. Finally, an example is given to illustrate the effectiveness of the proposed control method.     

Improved delay-range-dependent stability criteria for linear systems with time-varying delays

This paper is concerned with the stability analysis of linear systems with time-varying delays in a given range. A new type of augmented Lyapunov functional is proposed which contains some triple-integral terms. In the proposed Lyapunov functional, the information on the lower bound of the delay is fully exploited. Some new stability criteria are derived in terms of linear matrix inequalities without introducing any free-weighting matrices. Numerical examples are given to illustrate the effectiveness of the proposed method.     

A delay decomposition approach to delay-dependent passivity analysis for interval neural networks with time-varying delay

This paper is concerned with delay-dependent passivity analysis for interval neural networks with time-varying delay. By decomposing the delay interval into multiple equidistant subintervals, new Lyapunov-Krasovskii functionals (LKFs) are constructed on these intervals. Employing these new LKFs, a new passivity criterion is proposed in terms of linear matrix inequalities, which is dependent on the size of the time delay. Finally, some numerical examples are given to illustrate the effectiveness of the developed techniques.     

Delay-dependent criteria for the robust stability of systems with time-varying delay

The problem of delay-dependent robust stability for systems with time-varying delay has been considered. By using the S-procedure and the Park's inequality in the recent issue, a delay-dependent robust stability criterion which is less conservative than the previous results has been derived for time-delay systems with time-varying structured uncertainties. The same idea has also been easily extended to the systems with nonlinear perturbations. Numerical examples illustrated the effectiveness and the improvement of the proposed approach.     

H-infinity control for networked control systems (NCS) with time-varying delays

This paper discusses H-infin it y state feedback control for a networked control system with time-varying delays.Based on the free-weighing matri x method,a delay-dependent stability criterion satisfying a prescribed H-infini ty norm bound is presented for an NCS with unknown,time-varying and bounded del ays.And then,the criterion is transformed into suffici ent conditions based on linear matrix inequalities f or H-infinity control.The conditions thus obtained a re also used to design an H-infinity state feed back controller.This design method is further extend ed to solve the design problem of robust H-infin ity state feedback control.A numerical example demo nstrates the validity of the method.     

H-infinity control for networked control systems （NCS） with time-varying delays

1Introduction Ina networkedcontrol system(NCS),a communicationnetwork connects sensors,actuators and controllers.AnNCS has many advantages over the point_to_pointcommunication of traditional control systems:fast and easymaintenance,low cost,greater flexibility,etc.Therefore,NCSs are increasingly being usedfor industrial control in avariety of fields[1,2].On the other hand,control loopsonthe communication network are closedin an NCS.Thetime delays that occur when information is transmitte…     

New delay-dependent stability results for discrete-time recurrent neural networks with time-varying delay

This paper studies the problem of stability analysis for discrete-time recurrent neural networks (DRNNs) with time-varying delays. By using the discrete Jensen inequality and the sector bound conditions, a new less conservative delay-dependent stability criterion is established in terms of linear matrix inequalities (LMIs) under a weak assumption on the activation functions. By using a delay decomposition method, a further improved stability criterion is also derived. It is shown that the newly obtained results are less conservative than the existing ones. Meanwhile, the computational complexity of the newly obtained stability conditions is reduced since less variables are involved. A numerical example is given to illustrate the effectiveness and the benefits of the proposed method.     

Robust stabilization of linear discrete-time systems with time-varying input delay

This paper presents a sufficient condition to stabilize linear discrete-time systems with time-varying input delay and model uncertainties. The key idea consists of applying Artstein’s reduction method and the scaled bounded real lemma; the robust stabilization problem is cast as a set of linear matrix inequalities on a transformed delay-free system. Hence, a novel convex characterization of the problem, an alternative to bilinear matrix inequalities in prior literature, is provided. Predictor-based controllers and robust state-feedback stabilization are particular cases of the proposal. Furthermore, numerical examples show that this proposal may improve tolerance against delay variations when compared to other methods available in literature.     

Improved delay-dependent stability criteria for systems with a delay varying in a range

This paper provides improved delay-dependent stability criteria for systems with a delay varying in a range. The criteria improve over some previous ones in that they have fewer matrix variables yet less conservatism, which is established theoretically. An example is given to show the advantages of the proposed results.     

Delay-dependent robust stabilization for a class of neutral systems with nonlinear perturbations

This note deals with the problem of stabilization/stability for neutral systems with nonlinear perturbations. A new stabilization/stability scheme is presented. Using improved Lyapunov functionals, less conservative stabilization/stability conditions are derived for such systems based on linear matrix inequalities (LMI). Numerical examples are provided to show that the proposed results significantly improve the allowed upper bounds of the delay size over some existing ones in the literature.     

New delay-dependent criterion for the stability of recurrent neural networks with time-varying delay

This paper is concerned with the global asymptotic stability of a class of recurrent neural networks with interval time-varying delay. By constructing a suitable Lyapunov functional, a new criterion is established to ensure the global asymptotic stability of the concerned neural networks, which can be expressed in the form of linear matrix inequality and independent of the size of derivative of time varying delay. Two numerical examples show the effectiveness of the obtained results. Supported by the National Natural Science Foundation of China (Grant Nos. 60534010, 60728307, 60774048, 60774093), the Program for Cheung Kong Scholars and Innovative Research Groups of China (Grant No. 60521003) and the National High-Tech Research & Development Program of China (Grant No. 2006AA04Z183), China Postdoctoral Sciencer Foundation (Grant No. 20080431150), and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 200801451096)     

Stability analysis of networked control systems with time-varying sampling periods

In this paper, we present an interval model of networked control systems with time-varying sampling periods and time-varying network-induced delays and discuss the problem of stability of networked control systems using Lyapunov stability theory. A sufficient stability condition is obtained by solving a set of linear matrix inequalities. In the end, the illustrative example demonstrates the correctness and effectiveness of the proposed approach.     

New delay-dependent stability criteria for systems with interval delay

This paper provides a new delay-dependent stability criterion for systems with a delay varying in an interval. With a different Lyapunov functional defined, a tight upper bound of its derivative is given. The resulting criterion has advantages over some previous ones in that it involves fewer matrix variables but has less conservatism, which is established theoretically. Examples are provided to demonstrate the advantage of the stability result.     

New delay-dependent exponential stability criteria for neural networks with discrete and distributed time-varying delays

In this paper, the problem of exponential stability criteria for neural networks with discrete and distributed time-varying delays are considered. By dividing the discrete delay interval into multiple segments and choosing a new class of Lyapunov functional which contains tripe-integral terms, some new delay-dependent stability criteria are derived in terms of linear matrix inequalities. 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.     

New LMT-based delay-dependent criterion for global asymptotic stability of cellular neural networks

The problem of global asymptotic stability analysis is studied for a class of cellular neural networks with time-varying delay. By defining a Lyapunov–Krasovskii functional, a new delay-dependent stability condition is derived in terms of linear matrix inequalities. The obtained criterion is less conservative than some previous literature because free-weighting matrix method and the Jensen integral inequality are considered. Three illustrative examples are given to demonstrate the effectiveness of the proposed results.     

New results on robust exponential stability for discrete recurrent neural networks with time-varying delays

This paper is concerned with the problem of robust exponential stability analysis for uncertain discrete recurrent neural networks with time-varying delays. In terms of linear matrix inequality (LMI) approach, some novel stability conditions are proposed via a new Lyapunov function. Neither any model transformation nor free-weighting matrices are employed in our theoretical derivation. The established stability criteria significantly improve and simplify some existing stability conditions. Numerical examples are given to demonstrate the effectiveness of the proposed methods.