Global Passivity Analysis of Interval Neural Networks with Discrete and Distributed Delays of Neutral Type

This paper is concerned with delay-dependent passivity analysis for delayed neural networks (DNNs) of neutral type. We first discuss the passivity conditions for DNNs without uncertainties and then extend this result to the case of interval uncertainties. By partitioning the delay intervals into multiple equidistant subintervals, some appropriate Lyapunov-Krasovskii functionals (LKFs) are constructed on these intervals. Considering these new LKFs and using free-weighting matrix approach, several new passivity criteria are proposed in terms of linear matrix inequalities, which are dependent on the size of the time delay. Finally, five numerical examples are given to illustrate the effectiveness and less conservatism of the developed techniques.     

Stability analysis of uncertain neutral systems with discrete and distributed delays via the delay partition approach

This paper focuses on the stability analysis for neutral systems with discrete and distributed constant time-delays. Lyapunov-Krasovskii functionals (LKFs) are constructed by non uniformly dividing the whole delay interval into multiple segments and choosing proper functionals with different weighting matrices coressponding to different segments in the LKFs. By employing these LKFs, some new delay-derivative-dependent stability criteria are established for the neutral system in the delay partition approach. By utilizing the delay partition approach, the obtained stability criteria are stated in terms of linear matrix inequalities. Finally, some numerical examples are provided to illustrate the effectiveness of the proposed approach less conservative than the existing ones.     

Delay Dependent Exponential Stability for Fuzzy Recurrent Neural Networks with Interval Time-Varying Delay

In this paper, the problem of delay-dependent exponential stability for fuzzy recurrent neural networks with interval time-varying delay is investigated. The delay interval has been decomposed into multiple non equidistant subintervals, on these interval Lyapunov-Krasovskii functionals (LKFs) are constructed to study stability analysis. Employing these LKFs, an exponential stability criterion is proposed in terms of Linear Matrix Inequalities (LMIs) which can be easily solved by MATLAB LMI toolbox. Numerical example is given to illustrate the effectiveness of the proposed method.     

New conditions for delay-derivative-dependent stability

Two recent Lyapunov-based methods have significantly improved the stability analysis of time-delay systems: the delay-fractioning approach of Gouaisbaut and Peaucelle (2006) for systems with constant delays and the convex analysis of systems with time-varying delays of Park and Ko (2007). In this paper we develop a convex optimization approach to stability analysis of linear systems with interval time-varying delay by using the delay partitioning-based Lyapunov–Krasovskii Functionals (LKFs). Novel LKFs are introduced with matrices that depend on the time delays. These functionals allow the derivation of stability conditions that depend on both the upper and lower bounds on delay derivatives.     

New results on stability analysis of singular time-delay systems

This paper deals with the problem of delay-dependent stability analysis for singular systems with a constant time delay. By employing the Jensen inequality and the Wirtinger-based inequality, new delay-dependent stability criteria are developed. Furthermore, in order to obtain less conservative results, a new method of constructing Lyapunov--Krasovskii functionals (LKFs) is used. It should be pointed out that the positive-definiteness restrictions on some symmetric matrices of the LKFs are removed. All the criteria are proposed in terms of strict linear matrix inequalities. Finally, numerical examples are given to demonstrate the less conservatism of the results.     

Passivity and robust synchronisation of switched interval coupled neural networks with time delay

This paper is concerned with passivity and robust synchronisation of switched coupled neural networks with uncertain parameters. First, the mathematical model of switched coupled neural networks with interval uncertain parameters is established, which consists of L modes and switches from one mode to another according to the switching rule. Second, by employing passivity theory and linear matrix inequality techniques, delay-independent and delay-dependent conditions are derived to guarantee the passivity of switched interval coupled neural networks. Moreover, based on the proposed passivity results, global synchronisation criteria can be obtained for switched coupled neural networks with or without uncertain parameters. Finally, an illustrative example is provided to demonstrate the effectiveness of the obtained results.     

Passivity analysis for neural networks with a time-varying delay

This paper deals with the problem of passivity analysis for neural networks with both time-varying delay and norm-bounded parameter uncertainties by employing an improved free-weighting matrix approach. Some useful terms have been retained, which were used to be ignored in the derivative of Lyapunov-Krasovskii functional. Furthermore, the relationship among the time-varying delay, its upper bound and their difference is taken into account. As a result, for two types of time-varying delays, less conservative delay-dependent passivity conditions are obtained in terms of linear matrix inequalities (LMIs), respectively. Finally, a numerical example is given to demonstrate the effectiveness of the proposed techniques.     

Synchronization of bilateral teleoperators with time delay

Bilateral teleoperators, designed within the passivity framework using concepts of scattering and two-port network theory, provide robust stability against constant delay in the network and velocity tracking, but cannot guarantee position tracking in general. In this paper we fundamentally extend the passivity-based architecture to guarantee state synchronization of master/slave robots in free motion independent of the constant delay and without using the scattering transformation. We propose a novel adaptive coordination architecture which uses state feedback to define a new passive output for the master and slave robots containing both position and velocity information. A passive coordination control is then developed which uses the new outputs to state synchronize the master and slave robots in free motion. The proposed algorithm also guarantees ultimate boundedness of the master/slave trajectories on contact with a passive environment. Experimental results are also presented to verify the efficacy of the proposed algorithms.     

A generalized approach to stabilization of linear interconnected time‐delay systems

The objective of this paper is to propose a generalized approach to stabilization of systems which are composed of linear time‐delay subsystems coupled by linear time‐varying interconnections. The proposed algorithms, which are formulated within the convex optimization framework, provide decentralized solutions to the problem of delay‐dependent asymptotic stability with strict dissipativity. It is established that the new methodology can reproduce earlier results on passivity, positive realness and disturbance attenuation. Then a decentralized structure of dissipative state‐feedback controllers is designed to render the closed‐loop interconnected system delay‐dependent asymptotically stable with strict dissipativity. Numerical examples are presented to illustrate the applicability of the design method. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

New delay dependent robust stability criteria for T-S fuzzy systems with constant delay

This paper deals with the problem of delay dependent robust stability for T-S fuzzy time delay systems. The approach based on constructing a new Lyapunov-Krasovskii functional by dividing uniformly the delay interval into N segment with N is positive integer, and using Finsler’s lemma. This new Lyapunov-Krasovskii functional is chosen with different weighted matrices corresponding to different segments. The perturbations considered are norm bounded, and the results are expressed in terms of linear matrix inequality (LMIs). Numerical examples are provided to show the effectiveness of the present method, compared with some recent previous ones.     

Optimal partitioning method for stability analysis of continuous/discrete delay systems

This paper is concerned with the problem of stability analysis for continuous‐time/discrete‐time systems with interval time‐varying delay. Based on the idea of partitioning the delay interval into l nonuniform subintervals, new Lyapunov functionals are established. By utilizing the reciprocally convex approach to deal with the delay information in each subinterval, sufficient stability conditions are proposed in terms of linear matrix inequalities. Based on these criteria, the optimal partitioning method is given on the basis of the genetic algorithm. Finally, the reduced conservatism of the results in this paper is illustrated by numerical examples. Copyright © 2013 John Wiley & Sons, Ltd.     

Stability of systems with uncertain delays: a new "Complete" Lyapunov-krasovskii functional

Stability of linear systems with uncertain time-varying delay is considered in the case, where the nominal value of the delay is constant and nonzero. Recently a new construction of Lyapunov-Krasovskii functionals (LKFs) has been introduced: To a nominal LKF, which is appropriate to the system with nominal delays, terms are added that correspond to the perturbed system and that vanish when the delay perturbations approach 0. In the present note we combine a "complete" nominal LKF, the derivative of which along the trajectories depends on states and their derivatives, with the additional terms depending on the delay perturbation. The new method is applied to the case of multiple uncertain delays with one nonzero nominal value. Numerical examples illustrate the efficiency of the method.     

Finite-time boundedness of state estimation for semi-Markovian jump systems with distributed leakage delay and linear fractional uncertainties

In this paper, the problem of finite-time bounded control for uncertain semi-Markovian jump neural networks with mixed delays which include distributed leakage delay (DLD) and mixed time-varying delays is considered. The system not only contains semi-Markovian jump, linear fractional uncertainties (LFUs), mixed time-varying delays but also includes distributed time delays in the leakage term which is not yet investigated in existing papers. Firstly, uncertainty parameters in the systems are solved by LFU based on the new model. Secondly, a novel augmented Lyapunov–Krasovskii functional (LKF) which involves more information about time-varying delays is constructed. Moreover, latest integral inequalities and time-delays division method are used to estimate the derivative of proposed LKFs. Thirdly, in the framework of uncertainty, semi-Markovian jump, DLD, mixed delays and external disturbance, a full-order state estimator is constructed such that the error dynamic system is finite-time bounded under the condition of given linear matrix inequalities. Finally, usefulness and advantages of the obtained results are verified by three numerical examples.     

The effect of system response delay and delay variability on inexperienced videotex users

To test the effects of system response delay and delay variability on users of videotex it was decided to experiment in a context close to that of the service under consideration. Accordingly 165 subjects were drawn from the general public to try videotex in a series of four experiments. An emphasis on performance-related outcome measures was deemed inappropriate. Accordingly, a strategy using stepwise multiple regression followed by factor analysis selected 11 important variables from an original 38. Then these were clustered into four linear combinations or scales labelled session length, passivity, speed of response and difficulty. All four experiments failed to find any significant effects due to mean response delay. Two of the three experiments that tested ranges of randomized delay with rectangular distributions found significant disruptive effects on users. These results replicate earlier studies, and extend their generality to the context of naive users of videotex. The results also support the concept of using response-style scales rather than performance measures in non-work settings, and they contribute to the construct validity of the scales.     

基于时滞分割法的区间变时滞不确定系统鲁棒稳定新判据

针对一类存在泛数有界不确性的区间变时滞线性系统, 利用Lyapunov-Krasovskii (L-K) 泛函方法并结合线性矩阵不等式(LMI) 技术建立一种新的保守性更低的鲁棒稳定性判据. 首先基于时滞分割方法将时滞区间均分成N 等分, 针对不同的子区间构造合适的L-K 泛函; 然后在各自的分割区间采用保守性较小的积分不等式处理泛函沿时间的导数, 基于凸组合技术建立了LMI 形式的时滞相关稳定性新判据; 最后通过数值实例验证了结论的有效性.

     

滞后神经网络新的时滞相关无源判定准则

研究了一类含有时变时滞的神经网络无源分析问题。通过将时滞区间分解为两个子区间和构造新颖的Lyapunov泛函,得到了基于LMIs(线性矩阵不等式)形式的时滞相关无源的新准则。这个新准则推广了一些已有的结果,并且具有更少的保守性。最后,数值例子和仿真验证了结论的有效性。     

A delay decomposition approach to delay‐dependent stability for linear systems with time‐varying delays

This paper is concerned with delay‐dependent stability for linear systems with time‐varying delays. By decomposing the delay interval into multiple equidistant subintervals, on which different Lyapunov functionals are chosen, and new Lyapunov‐Krasvskii functionals are then constructed. Employing these new Lyapunov‐Krasvskii functionals, some new delay‐dependent stability criteria are established. The numerical examples show that the obtained results are less conservative than some existing ones in the literature. Copyright © 2009 John Wiley & Sons, Ltd.     

Bilateral control of teleoperators with time delay

A control law for teleoperators is presented which overcomes the instability caused by time delay. By using passivity and scattering theory, a criterion is developed which shows why existing bilateral control systems are unstable for certain environments, and why the proposed bilateral control law is stable for any environment and any time delay. The control law has been implemented on a single-axis force-reflecting hand controller, and preliminary results are shown. To keep the presentation clear, a single-degree-of-freedom (DOF) linear time-invariant (LTI) teleoperator system is discussed. Nevertheless, results can be extended, without loss of generality, to an n-DOF nonlinear teleoperation system     

A separation method of transmission delays and data packet dropouts from a lumped input delay in the stability problem of networked control systems

This paper proposes a separation method of a transmission delay and data packet dropouts from a lumped input delay in the stability problem of a networked control system, where both the transmission delay and the data packet dropouts are involved. By modeling data packet dropouts as sampling processes and the transmission delay as a state delay, the networked control system is represented as a sampled‐data system with aperiodic sampling and a state delay. In order to separate the state delay and the sampling, the sampled‐data system is transformed into a new system with an integral operator, where the sampling is embedded into the integral operator. By investigating the integral operator's gain and passivity, a novel Lyapunov functional is constructed to address the stability problem. The obtained stability results are dependent on both the data packet dropouts and the time delay. A numerical example is provided to demonstrate that the stability results are less conservative than some existing ones. Copyright © 2016 John Wiley & Sons, Ltd.