Easily testable necessary and sufficient algebraic criteria for delay-independent stability of a class of neutral differential systems

This paper analyzes the eigenvalue distribution of neutral differential systems and the corresponding difference systems, and establishes the relationship between the eigenvalue distribution and delay-independent stability of neutral differential systems. By using the “Complete Discrimination System for Polynomials”, easily testable necessary and sufficient algebraic criteria for delay-independent stability of a class of neutral differential systems are established. The algebraic criteria generalize and unify the relevant results in the literature. Moreover, the maximal delay bound guaranteeing stability can be determined if the systems are not delay-independent stable. Some numerical examples are provided to illustrate the effectiveness of our results.     

LMI characterization of the strong delay-independent stability of linear delay systems via quadratic Lyapunov–Krasovskii functionals

In this note is proposed an analogue for linear delay systems of the characterization of asymptotic stability of the rational systems by the solvability of associated Lyapunov equation. It is shown that strong delay-independent stability of delay system is equivalent to the feasibility of certain linear matrix inequality (LMI), related to quadratic Lyapunov–Krasovskii functionals.     

线性时滞系统时滞独立稳定的充分条件

利用Lyapunov稳定性理论，通过一个推广的Lyapunov矩阵方程得出时滞独立稳定的充分条件，基于这个充分条件建立了几个判定线性时滞系统稳定性的简单判据，并推导出系统具有任意指定收敛速度指数稳定的充分条件。计算例子说明了所得结果的有效性。     

具有时变时滞的线性大系统的稳定条件

通过对系统微分方程解的估计,讨论一类具有时变时滞的线性大系统的稳定性,所导出的稳定性判别条件包括系统与时滞无关和与时滞相关稳定的充分条件,然后讨论了大系统的鲁棒稳定条件,并与相关文献进行比较,计算实例表明,所得出的结果改进了现有文献的研究结果。     

Stability of linear multistep methods for delay integro-differential equations

This paper is concerned with the numerical solution of delay integro-differential equations. The adaptation of linear multistep methods is considered. The emphasis is on the linear stability of numerical methods. It is shown that every A-stable, strongly 0-stable linear multistep method of Pouzet type can preserve the delay-independent stability of the underlying linear systems. In addition, some delay-dependent stability conditions for the stability of numerical methods are also given.     

高阶时滞多智能体系统一致性控制

本文讨论了多输入网络化时滞多智能体系统的一致性问题.应用无向或有向图描述网络化系统的拓扑结构.多智能体的一致性收敛问题可以转化为线性时滞系统的稳定性问题.通过双线性矩阵不等式可以得到高阶多智能体系统时滞相依以及时滞独立的一致性准则.最后,举例一个无向拓扑结构的时滞多智能体来说明本文方法的有效性.     

力反馈时延遥操作系统的时延相关稳定性分析

当力反馈双边控制系统的主从端之间存在时延时,系统的稳定性和透明性会遭到破坏.无源性方法能保证系统的时延无关稳定性,但由于稳定性和透明性冲突,系统的透明性较差.本文利用绝对稳定性理论推导出一种新的双边控制算法.它以时延相关稳定性代替时延无关稳定性作为控制设计的目标,牺牲一部分不必要的稳定裕度以改善系统的透明性.它在保证系统稳定性的前提下使系统具有更好的透明性,最后用仿真进行了验证.     

Further remarks on asymptotic stability and set invariance for linear delay-difference equations

We studied the existence of positively invariant sets for linear delay-difference equations. In particular, we regarded two strong stability notions: robust (with respect to delay parameter) asymptotic stability for the discrete-time case and delay-independent stability for the continuous-time case. The correlation between these stability concepts is also considered. Furthermore, for the delay-difference equations with two delay parameters, we provided a computationally efficient numerical routine which is necessary to guarantee the existence of contractive sets of Lyapunov–Razumikhin type. This condition also appears to be necessary and sufficient for the delay-independent stability and sufficient for the robust asymptotic stability.     

Stability of switched positive linear delay systems with mixed impulses

ABSTRACT

This paper investigates the global exponential stability of both continuous-time and discrete-time switched positive linear delay systems with the coexistence of destabilising and stabilising impulses. Based on the comparison principle, with the help of discretised multiple linear copositive Lyapunov functions, some delay-independent stability results are obtained. It should be noted that it is the first time that discrete-time switched delay systems with asynchronous switching and impulses are considered, and the switching effect can be stabilising in the obtained results of this paper. Some numerical examples are provided to demonstrate the effectiveness and superiority of the derived results.     

Delay-independent exponential stability criteria for time-varyingdiscrete delay systems

Derives delay-independent exponential stability conditions for linear/nonlinear time-varying discrete delay systems. Since these conditions are of delay-independence and easily verifiable, they may provide handy tools for the stability analysis     

Delay-dependent stability of reset systems

This work presents results on the stability of time-delay systems under reset control. The case of delay-dependent stability is addressed, by developing a generalization of previous stability results for reset systems without delay, and also a generalization of the delay-independent case. The stability results are derived by using appropriate Lyapunov-Krasovskii functionals, obtaining LMI (Linear Matrix Inequality) conditions and showing connections with passivity and positive realness. The stability conditions guarantee that the reset action does not destabilize the base LTI (Linear Time Invariant) system. Several interpretations are given for these conditions in terms of impulsive control, which provide insights into the potentials of reset control.     

Stability of perturbed systems with time-varying delays

This paper gives easily verifiable sufficient conditions of robust asymptotic stability of linear time-delay systems subject to parametric unstructured or highly-structured perturbations. The criteria given in this paper are delay-independent or delay-dependent. The considered delay may be time-varying. An estimation of the transient behaviour of the studied systems is also provided (exponential rate of convergence).Scalar or vectorial inequalities involving Hurwitz matrices, matrix measures and norms constitute the mathematical foundations of the exposed results.     

Robust stability of uncertain time-delay systems

This paper presents several sufficient conditions, delay-independent or delay-dependent, that guarantee the robust stability of uncertain time-delay systems subjected to parametric perturbations. Both single and composite uncertain systems with one delayed state are considered and each of these results, expressed by a succinct scalar inequality, permits the assessment of the transient behaviour of uncertain systems. The robustness of the time-delay system with respect to delay uncertainty is also discussed. Furthermore, these results are extended to the perturbed systems with multiple non-commensurate time delays. It is shown that the parameter perturbations may destabilize the system; hence the nominal system should be sufficiently stable to ensure robust stability.     

Robust stability of uncertain large-scale systems with time delay

In this paper, the Lyapunov functional has been used to study the robust stability of uncertain large-scale systems with time delay; some new delay-independent conditions for stability of these uncertain large-scale systems are obtained. Finally, some examples are given to illustrate our results and to compare with previous results.     

A distributed controller approach for delay-independent stability of networked control systems

This article introduces a novel distributed controller approach for networked control systems (NCS) to achieve finite gain L₂ stability independent of constant time delay. The proposed approach represents a generalization of the well-known scattering transformation which applies for passive systems only. The main results of this article are (a) a sufficient stability condition for general multi-input-multi-output (MIMO) input-feedforward-output-feedback-passive (IF-OFP) nonlinear systems and (b) a necessary and sufficient stability condition for linear time-invariant (LTI) single-input-single-output (SISO) systems. The performance advantages of the proposed approach are reduced sensitivity to time delay and improved steady state error compared to alternative known delay-independent small gain type approaches. Simulations validate the proposed approach.     

Input-to-state stability analysis for interconnected difference equations with delay

Input-to-state stability (ISS) of interconnected systems with each subsystem described by a difference equation subject to an external disturbance is considered. Furthermore, special attention is given to time delay, which gives rise to two relevant problems: (i) ISS of interconnected systems with interconnection delays, which arise in the paths connecting the subsystems, and (ii) ISS of interconnected systems with local delays, which arise in the dynamics of the subsystems. The fact that a difference equation with delay is equivalent to an interconnected system without delay is the crux of the proposed framework. Based on this fact and small-gain arguments, it is demonstrated that interconnection delays do not affect the stability of an interconnected system if a delay-independent small-gain condition holds. Furthermore, also using small-gain arguments, ISS for interconnected systems with local delays is established via the Razumikhin method as well as the Krasovskii approach. A combination of the results for interconnected systems with interconnection delays and local delays, respectively, provides a framework for ISS analysis of general interconnected systems with delay. Thus, a scalable ISS analysis method is obtained for large-scale interconnections of difference equations with delay.     

直流微电网分布式控制的时滞稳定化设计

直流微电网中,大部分控制器在设计时未考虑通信延时对系统性能的影响,这可能会导致控制器在实际应用中失效甚至影响系统的稳定性.本文基于一种分布式控制策略,建立了直流微电网系统的时滞模型,重点研究了通信延时对系统稳定性的影响.结合Razumikhin稳定性理论,提出了一种针对时变时滞系统的全时滞稳定性判据.为了更加适用于实际系统,在另一种全时滞稳定性判据的基础上,对系统时滞相关稳定性进行分析,得到保证系统稳定的延时上界,进而给出了一种确定控制参数范围的方法.与传统的将通信延时处理为一阶惯性环节的分析方法相比,基于时滞系统的分析方法更切合实际,为系统的稳定运行提供了一个更宽的时滞范围,提高了系统的可靠性.仿真和实验结果表明本文提出的控制参数设计方法能保证系统在最大延时下的稳定运行.     

Delay-Independent Stability Conditions for Time-Varying Nonlinear Uncertain Systems

A new stability criterion for time-varying systems consisting of linear and norm bounded nonlinear terms with uncertain time-varying delays is formulated. An explicit delay-independent sufficient stability condition is formulated in the terms of the transition matrix of the given linear part without delay and the bounds for the uncertain terms. The obtained condition turns out to be also necessary if the matrix of the linear part is time-invariant and symmetric; it is shown that these systems satisfy the well-known Aizerman's conjecture. The obtained criterion is contrasted by some of stability estimates available in the literature for these kinds of systems; in all cases the proposed criterion provides less conservative stability bounds.     

Effect of transmission delay on the rate of convergence of a classof nonlinear contractive dynamical systems

We investigate the qualitative properties of a general class of contractive dynamical systems with time delay by using a unified analysis approach for any p-contraction with p in [1,infinity]. It is proved that the delayed contractive dynamical system is always globally exponentially stable no matter how large the time delay is, while the rate of convergence of the delayed system is reduced as the time delay increases. A lower bound on the rate of convergence of the delayed contractive dynamical system is obtained, which is the unique positive solution of a nonlinear equation with three parameters, namely, the time delay, the time constant and the p-contraction constant in the system. We show that the previously established results in the literature about the global asymptotic or exponential stability independent of delay for Hopfield-type neural networks can actually be deduced by recasting the network model into the general framework of contractive dynamical systems with some p-contraction (p in [1,infinity]) under the given delay-independent stability conditions. Numerical simulation examples are also presented to illustrate the obtained theoretical results.