Absolute stability of nonlinear systems with two additive time-varying delay components

In this paper, we present a new sufficient condition for absolute stability of Lure system with two additive time-varying delay components. This criterion is expressed as a set of linear matrix inequalities (LMIs), which can be readily tested by using standard numerical software. We use this new criterion to stabilize a class of nonlinear time-delay systems. Some numerical examples are given to illustrate the applicability of the results using standard numerical software.     

Stability analysis for continuous systems with two additive time-varying delay components

This paper presents a new result of stability analysis for continuous systems with two additive time-varying delay components, which represent a general class of delay systems with strong application background in network based control systems. This criterion is expressed as a set of linear matrix inequalities, which can be readily tested by using standard numerical software. A numerical example is provided to show the effectiveness and advantage of the proposed stability condition.     

Delay-range-dependent stability criterion for interval time-delay systems with nonlinear perturbations

In this paper, we consider the problem of robust stability for a class of linear systems with interval time-varying delay under nonlinear perturbations using Lyapunov-Krasovskii (LK) functional approach. By partitioning the delay-interval into two segments of equal length, and evaluating the time-derivative of a candidate LK functional in each segment of the delay-interval, a less conservative delay-dependent stability criterion is developed to compute the maximum allowable bound for the delay-range within which the system under consideration remains asymptotically stable. In addition to the delay-bi-segmentation analysis procedure, the reduction in conservatism of the proposed delay-dependent stability criterion over recently reported results is also attributed to the fact that the time-derivative of the LK functional is bounded tightly using a newly proposed bounding condition without neglecting any useful terms in the delay-dependent stability analysis. The analysis, subsequently, yields a stable condition in convex linear matrix inequality (LMI) framework that can be solved non-conservatively at boundary conditions using standard numerical packages. Furthermore, as the number of decision variables involved in the proposed stability criterion is less, the criterion is computationally more effective. The effectiveness of the proposed stability criterion is validated through some standard numerical examples.     

Stability analysis of discrete-time systems with additive time-varying delays

In this paper, the problem of stability analysis of discrete-time delay systems with two additive time-varying delays is considered. A new stability result is derived for a general class of delay systems which has practical application background in networked control systems . The stability criterion is expressed in the form of linear matrix inequalities (LMIs), which can be readily solved by using standard numerical software. An illustrative example is provided to show the advantage of the proposed stability condition.     

奇异时滞系统的时滞依赖稳定性判据

讨论了奇异时滞系统的稳定性问题. 首先, 在几个最新的结果之间建立了等价性, 并给出了一个简化的稳定性判据. 然后, 通过使用时滞分解的方法, 得到了一个新的稳定性判据. 它比现有结果具有更少的保守性. 最后, 给出了一个数值例子, 表明了新判据是有效的且保守性较小.     

Stability results for stochastic bidirectional associative memory neural networks with multiple discrete and distributed time-varying delays

This paper is concerned with the global asymptotic stability of a class of stochastic bidirectional associative memory neural networks with both multiple discrete and distributed time-varying delays. A new criterion of asymptotic stability is derived in terms of linear matrix inequality, which can be efficiently solved by a standard numerical software. An illustrative numerical example is also given to show the applicability and effectiveness of the proposed results.     

Improved asymptotical stability criteria for static recurrent neural networks

In this paper, the problem of asymptotical stability for static recurrent neural networks is investigated. Based on delay partitioning approach and a new Lyapunov–Krasvoskii functional, delay-independent conditions are proposed to ensure the asymptotic stability of the static recurrent neural networks. The delay-independent conditions are less conservative than the existing ones. Expressed in linear matrix inequalities, the stability conditions can be checked using the standard numerical software. Two numerical examples are provided to illustrate the effectiveness and the reduced conservatism of the proposed results.     

Novel delay‐derivative‐dependent stability criteria using new bounding techniques

This paper studies the stability of linear systems with interval time‐varying delays. By constructing a new Lyapunov–Krasovskii functional, two delay‐derivative‐dependent stability criteria are formulated by incorporating with two different bounding techniques to estimate some integral terms appearing in the derivative of the Lyapunov–Krasovskii functional. The first stability criterion is derived by using a generalized integral inequality, and the second stability criterion is obtained by employing a reciprocally convex approach. When applying these two stability criteria to check the stability of a linear system with an interval time‐varying delay, it is shown through some numerical examples that the first stability criterion can provide a larger upper bound of the time‐varying delay than the second stability criterion. Copyright © 2012 John Wiley & Sons, Ltd.     

中立型变时滞系统的鲁棒稳定性

考虑不确定中立型变时滞系统的鲁棒稳定性问题. 首先, 引入新的变量来代替系统的不确定性; 然后, 通过构造一般形式的Lyapunov-Krasovskii泛函、使用积分不等式并引入自由矩阵, 得到了基于线性矩阵不等式的系统稳定性判据. 该结论与中立型时滞, 离散时滞及其导数均相关, 具有较小的保守性. 最后, 通过仿真算例说明了所得到的结论在保守性上优于现存的结果以及中立型时滞, 离散时滞及其导数三者之间的关系.     

Delay-partitioning approach to stability analysis of state estimation for neutral-type neural networks with both time-varying delays and leakage term via sampled-data control

This paper mainly focuses on further improved stability analysis of state estimation for neutral-type neural networks with both time-varying delays and leakage delay via sampled-data control by delay-partitioning approach. Instead of the continuous measurement, the sampled measurement is used to estimate the neuron states and a sampled-data estimator is constructed. To fully use the sawtooth structure characteristics of the sampling input delay, sufficient conditions are derived such that the system governing the error dynamics is asymptotically stable. The design method of the desired state estimator is proposed. We construct a suitable Lyapunov–Krasovskii functional (LKF) with triple and quadruple integral terms then by using a novel free-matrix-based integral inequality (FMII) including well-known integral inequalities as special cases. Moreover, the design procedure can be easily achieved by solving a set of linear matrix inequalities (LMIs), which can be easily facilitated by using the standard numerical software. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed results.     

Stability analysis and stabilization of Markovian jump systems with time‐varying delay and uncertain transition information

The paper investigates the problems of stability and stabilization of Markovian jump systems with time‐varying delays and uncertain transition rates matrix. First, the stochastic scaled small‐gain theorem is introduced to analyze the stability of the Markovian jump system. Then, a new stability criterion is proposed by using a new Lyapunov‐Krasovskii functional combined with Wirtinger‐based integral inequality. The proposed stability condition is demonstrated to be less conservative than other existing results. The merit of the proposed approach lies in its reduced conservatism, which is made possible by a new precise triangle inequality and a new Lyapunov‐Krasovskii functional. Moreover, a controller design criterion is presented according to the stability criterion. Furthermore, the transition rate matrix is treated as partially known and with uncertainty, and the relevant stability and stabilization criteria are proposed. Finally, 3 numerical examples are provided to illustrate the superior result of the stability criteria and the effectiveness of the proposed controller design method.     

H∞ performance analysis for discrete‐time systems with additive time‐varying delays

The problem of stability analysis for discrete time‐delay systems with additive delays is considered. New results on stability and H_∞ performance are proposed for systems with two successive delay components. By exploiting new Lyapunov–Krasovskii functionals, the proposed results have a strong practical application background in networked control systems. The criteria are expressed in the form of linear matrix inequalities, which can be readily solved by using standard numerical software. Illustrative examples are provided to show the advantage of these results. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

时变时滞NCS控制器的改进设计

建立时滞差分不等式,得到网络化控制系统(NCS)的指数稳定判据,基于该判据设计NCS状态反馈控制器。该设计以线性矩阵不等式(LMI)形式给出,不包含任何自由矩阵,通过Matlab中的LMI工具箱进行求解。数值仿真结果表明,该设计具有计算量小、求解方便、保守性弱的特点。     

Delay-dependent absolute stability criterion for Lurie system with probabilistic interval time-varying delay

In this paper,the absolute stability of Lurie control system with probabilistic time-varying delay is studied. By using a new extended Lyapunov-Krasovskii functional,an improved stability criterion based on LMIs is presented and its solvability heavily depends on the sizes of both the delay range and its derivatives,which has wider application fields than those present results.The efficiency and reduced conservatism of the presented results can be demonstrated by two numerical examples with giving some comparing results.     

Stability analysis for linear delayed systems via an optimally dividing delay interval approach

This paper addresses the problem of stability for linear systems with time-varying delay. A novel augmented Lyapunov–Krasovskii functional is constructed by using the idea of optimally dividing the delay interval [0,τ(t)] into some variable sub-intervals and line integral technology. Using the novel augmented functional, the new delay-dependent stability criteria are proposed for linear systems with time-varying delay. The gain is that this stability criterion can lead to much less conservative stability results compared to other methods for linear systems with delay. Two numerical examples are provided to verify the effectiveness of the proposed criteria.     

Delay-dependent stability for discrete systems with large delay sequence based on switching techniques

This paper considers the exponential stability problem for a class of discrete time-varying delay systems with large delay sequences (LDSs). A new method based on a switching technique is presented to solve this problem. A switched delay system, in which one of the discrete subsystems may be unstable, is firstly employed to describe such a system, and then some new concepts about LDSs are introduced. Next, using a novel piecewise Lyapunov functional, explicit delay-dependent conditions are developed to show how long and how frequent the LDSs can be and still maintain the system exponentially stable. Without LDSs, the criterion obtained in this paper includes the established one as a special case. Two numerical examples are given to show the effectiveness of the proposed method.     

T-S模糊时滞系统的时滞相关镇定

基于T-S模糊模型方法,研究一类非线性区间时滞系统的稳定性分析与镇定问题,基于一组线性矩阵不等式的可解性,给出了非线性时滞系统时滞相关稳定和镇定的充分条件,并通过构造新的模糊权依赖型Lyapunov泛函,降低了稳定性准则的保守性,最后通过仿真例子表明了所提方法的有效性.     

New stability criterion for linear switched systems with time‐varying delay

This paper studies the stability problem of a class of linear switched systems with time‐varying delay in the sense of Hurwitz convex combination. By designing a parameter‐dependent switching law and using a new convex combination technique to deal with delay terms, a new stability criterion is established in terms of LMIs, which is dependent on the parameters of Hurwitz convex combination. The advantage of the new criterion lies in its less conservatism and simplicity. Numerical examples are given to illustrate the effectiveness and the less conservatism of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.     

A new approach to the discretization of continuous-time controllers

A new method for discretizing continuous-time controllers is derived, using principles of controller approximation. It focuses on the closed-loop use of the discrete-time controller. The resulting approximation criterion is a measure for stability of the control system, provides an upper bound on the sampling time for which stability can be guaranteed, and because it is based on continuous-time controller approximation it indicates the cost of discretization in terms of performance degradation. The discrete-time controller is obtained through minimization of this criterion, which can be performed with standard software used in H_∞ controller design     

Solving the Problem of Dynamic Adaptability of Artificial Intelligence Systems that Control Dynamic Technical Objects

This paper investigates the increase in the response speed and stability of artificial intelligence systems that control dynamic technical objects. The problem of calculating the optimal time of switching an artificial intelligence system between software classes by the criterion of the rigidity degree of the model of a control object is considered. The solution of this problem is proposed for the general case of the control object dynamics when the rigidity of the mathematical model can significantly change during functioning and it is necessary to dynamically determine the moment of transition from standard methods of numerical integration to specialized numerical methods intended for calculating rigid dynamic models.