时滞线性随机系统的均方稳定性与反馈镇定*

本文研究Ｉｔｏｏ型随机滞后系统的均方稳定性与反馈镇定。文中首先建立了Ｉｔｏ型随机滞后系统的新型稳定性定理，然后采用适当的Ｌｙａｐｕｎｏｖ泛函得到了时滞线性随机系统零解均方渐近稳定的一个充分性判据，该判据适用于完全滞后型的随机系统，据此判据，文中给出了时滞线性随机系统的滞后反馈镇定方法。     

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.     

时滞神经网络的全局渐近稳定性分析

研究一类具有时滞的细胞神经网络的稳定性问题,利用Lyapunov—Krasovskii泛函的方法,给出时滞相关的稳定性判据。稳定性判据是以线性矩阵不等式的形式给出,可以很容易得出时滞的上界。在得到时滞相关的稳定性判据的同时也可以得到时滞无关的稳定性判据。数值算例说明其结果的优越性。     

时变时滞离散广义Markov 跳变系统的鲁棒稳定性

研究一类具有区间时变时滞的离散不确定广义Markov跳变系统的时滞相关鲁棒稳定性问题.通过将Jensen不等式与一个新的定界不等式相结合,得到了一个新的稳定性判据,该判据中仅含有Lyapunov变量,具有较小的计算负担.进而,基于凸组合方法得到了另一个新的稳定性判据,该判据引入了一些自由矩阵变量,具有较小的保守性.数值算例表明了所提出方法的有效性.     

具有任意未知常时滞系统的鲁棒稳定性(英)

本文采用李雅普诺夫泛函法和一个矢量不等式建立了若干具有任意未知常时滞系统的鲁棒稳定性判据．所获得结果是时滞无关的、文中示例说明了所得稳定性判据减少了现存结果的保守性．     

具有任意未知常时滞系统的鲁棒稳定性

本文采用李雅普诺夫泛函法和一个矢量不式建立了若干具有任意未知常时滞系统的鲁棒稳定性判据，所获得结果是时无关的，文中示例说明了所得稳定性判据减少了现存结果的保守性。     

带时滞的线性时变奇异系统的稳定性

通过比较方法建立了一类带时滞的线性时变奇异系统的稳定性判据,并讨论了相应的带有时滞的时变区间奇异系统的稳定性,给出了一个稳定性的比较定理。     

基于划分时滞区间的一类Cohen-Grossberg神经网络的鲁棒稳定性

研究一类具有时变时滞及参数不确性的Cohen-Grossberg神经网络的鲁棒稳定性问题.应用划分时滞区间的思想构造了一个新的Lyapunov泛函,并以线性矩阵不等式的形式给出了平衡点全局鲁棒稳定性判据,新判据放松了时变时滞变化率必须小于1的限制.仿真结果进一步证明了所得结论的有效性.     

具有多个未知常时滞线性系统的时滞无关稳定性

本文针对线性时滞系统包括时滞在系统建立了时滞无关的稳定性判据，所考虑的时滞可以是多任意未知常时滞，故所得结果是对滞无关的，针对线性时滞大系统的一个说明例子比较证明了所建立的结果好于文献中存在的结果。     

一类含有时变时滞的不确定中立型Hopfield神经网络的鲁棒稳定性判据

针对一类不确定中立型时变时滞Hopfield神经网络的鲁棒稳定性问题, 构造了一个新Lyapunov-Krasovskii泛函, 并结合自由矩阵方法和牛顿—莱布尼茨公式, 得到了新的时滞相关稳定性判据. 该判据考虑了中立型时变时滞Hopfield神经网络中的参数不确定性, 所得结果以线性矩阵不等式(Linear matrix inequality, LMI)的形式给出, 容易验证. 最后, 通过两个数值算例验证了该结果的有效性及可行性. 该判据对丰富与完善中立型神经网络的稳定性理论体系, 具有积极的意义.     

Robust admissibility of time-varying singular systems with commensurate time delays

This paper addresses the problem of admissibility of time-varying singular systems with commensurate time delays. By introducing a new method to study the convergence of the fast sub-system, an admissibility condition is obtained in terms of linear matrix inequalities, which guarantees the considered time-varying singular delay system to be regular, impulse free and stable. Furthermore, a robust admissibility condition is proposed for the case when the time-varying system matrices admit the usual constant-plus-norm-bounded structure. It is theoretically established that the proposed robust admissibility condition is less conservative than the existing one in the literature. One of the important features of the results is that the inferred admissibility condition coincides with the usual stability condition for state-space delay systems. Moreover, the results are also applicable to the multiple rational delay case.     

时滞不确定组合大系统的鲁棒分散镇定

将Riccati方法扩展到具有状态和输入时滞的不确定组合系统,给出了系统经状态反馈分散二次镇定的一个充分条件并证明该条件的成立等价于一个LMI最优解的存在。利用LMI最优解,给出了分散控制器的设计方案。仿真结果表明了该方法的有效性。     

Further results on delay‐dependent robust stability conditions of uncertain neutral systems

This paper deals with the problem of robust stability analysis for uncertain neutral systems. In terms of a linear matrix inequality (LMI), an improved delay‐dependent asymptotic stability criterion is developed without using bounding techniques on the related cross product terms. Based on this, a new delay‐dependent LMI condition for robust stability is obtained. 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. Copyright © 2005 John Wiley & Sons, Ltd.     

一类含未建模动态和时滞系统的鲁棒二次镇定

研究一类同时含有参数摄动和未建模动态的线性时滞系统的鲁棒控制问题。获得了系统可二次镇定的充分条件,给出一种不依赖于系统时滞的状态反馈控制器设计方法,最后给出了计算示例。     

Robust Stability and Stabilization Criteria for Discrete Singular Time‐Delay LPV Systems

This paper is concerned with establishing robust stability and stabilization criteria for discrete singular time‐delay linear parameter varying (LPV) systems. Firstly, a robust stability criterion is obtained for this class of systems by a delay‐partition approach, and thereby a less conservative sufficient condition which guarantees discrete singular time‐delay LPV systems to be admissible is given. Secondly, a class of state feedback controllers for stabilizing discrete singular time‐delay LPV systems is designed. Finally, compared with existing results, the numerical results of several examples illustrate the effectiveness of the approach proposed in this paper. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

BIBO stability and stabilization of networked control systems with short time‐varying delays

This paper presents a robust control approach to solve the stability and stabilization problems for networked control systems (NCSs) with short time‐varying delays. A new discrete‐time linear uncertain system model is proposed to describe the NCS, and the uncertainty of the network‐induced delay is transformed into the uncertainty of the system matrix. Based on the obtained uncertain system model, a sufficient BIBO stability condition for the closed‐loop NCS is derived by applying the small gain theorem. The obtained stability condition establishes a quantitative relation between the BIBO stability of the closed‐loop NCS and two delay parameters, namely, the delay upper bound and the delay variation range bound. Moreover, design procedures for the state feedback stabilizing controllers are also presented. An illustrative example is provided to demonstrate the effectiveness of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd.     

Generalized criteria on delay‐dependent stability of highly nonlinear hybrid stochastic systems

Our recent paper (Fei W, etal. Delay dependent stability of highly nonlinear hybrid stochastic systems. Automatica. 2017;82:165‐170) is the first to establish delay‐dependent criteria for highly nonlinear hybrid stochastic differential delay equations (SDDEs) (by highly nonlinear, we mean that the coefficients of the SDDEs do not have to satisfy the linear growth condition). This is an important breakthrough in the stability study as all existing delay stability criteria before could only be applied to delay equations where their coefficients are either linear or nonlinear but bounded by linear functions (namely, satisfy the linear growth condition). In this continuation, we will point out one restrictive condition imposed in our earlier paper. We will then develop our ideas and methods there to remove this restrictive condition so that our improved results cover a much wider class of hybrid SDDEs.     

Robust Stability For Uncertain Discrete Singular Systems With State Delay

A computationally simple stability condition for discrete singular systems with state delay is presented in this paper. Based on this, a robust stability result for such systems with structured parametric uncertainties is given. This condition ensures that, for all admissible uncertainties, the system under consideration is regular, causal and stable. Then D‐stability results for discrete singular delay systems are obtained. All the proposed conditions are easy to test.     

Delay‐dependent stability and stabilization of neutral time‐delay systems

This paper is concerned with the problem of stability and stabilization of neutral time‐delay systems. 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. On the basis of the obtained stability condition, a stabilizing method is also proposed. Using an iterative algorithm, the state feedback controller can be obtained. Numerical examples illustrate that the proposed methods are effective and lead to less conservative results. Copyright © 2008 John Wiley & Sons, Ltd.     

Consensus Seeking for Discrete-time Multi-agent Systems with Communication Delay

This paper studies the consensus problem for discrete-time multi-agent systems of first-order in the presence of constant communication delay. Provided that the agent dynamics is unstable and the network topology is undirected, effects of two kinds of communication delays on consensus are investigated. When the relative information is affected by delay, we show that the effect of delay can be alleviated by using the historical input information in the protocol design. On the other hand, if the communication delay only influences the actually transmitted information, sufficient condition admitting any large yet bounded delay for consensus is obtained, and the delay in this case is allowed to be unknown and time-varying. Finally, simulation results are provided to demonstrate the effectiveness of the theoretical results.