Less conservative delay-dependent stability criteria for linear systems with interval time-varying delays

This article provides new delay-dependent stability criteria for linear systems with interval time-varying delays. With a new Lyapunov–Krasovskii functional constructed, a tighter upper bound of its derivative is estimated. The resulting criterion has an advantage over some existing ones in the literature due to the fact that it involves fewer matrix variables and is less conservative, which is established theoretically. Two numerical examples are given to demonstrate the reduced conservatism of the proposed results.     

Delay-independent stability criteria for linear continuous systems with time-varying delays

New stability criteria for linear continuous systems with multiple time-varying delays are established by the Lyapunov function approach based on a new stability theorem for general type of retarded dynamical systems. A new technique for estimating the derivative of Lyapunov function along the solution of system at some specific instants is used so that the case of multiple time-varying delays can be dealt with less conservatively. In addition, (i) every criterion has only one tuning parameter matrix P>0 as the Lyapunov-type stability criterion for the corresponding linear continuous system without delays does; (ii) all the criteria are given in LMI forms and hence they are numerically tractable. It is remarked that the established criteria are less conservative than the existing ones in the literature. Three examples are given to illustrate the proposed method and to show the superiority of the obtained results to the existing ones in the literature.     

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.     

New stability criteria for linear systems with interval time-varying delay

This paper investigates robust stability of uncertain linear systems with interval time-varying delay. The time-varying delay is assumed to belong to an interval and is a fast time-varying function. The uncertainty under consideration includes polytopic-type uncertainty and linear fractional norm-bounded uncertainty. A new Lyapunov-Krasovskii functional, which makes use of the information of both the lower and upper bounds of the interval time-varying delay, is proposed to drive some new delay-dependent stability criteria. In order to obtain much less conservative results, a tighter bounding for some term is estimated. Moreover, no redundant matrix variable is introduced. Finally, three numerical examples are given to show the effectiveness of the proposed stability criteria.     

Robust stability criteria for uncertain linear systems with interval time-varying delay

This paper considers the robust delay-dependent stability problem of a class of linear uncertain system with interval time-varying delay and proposes less conservative stability criteria for computing the maximum allowable bound of the delay range. Less conservatism of the proposed stability criteria is attributed to the delay-central point method of stability analysis, wherein the delay interval is partitioned into two subintervals of equal length, and the time derivative of a candidate Lyapunov-Krasovskii functional based on delay decomposition technique is evaluated in each of these delay segments. In deriving the stability conditions in LMI framework, neither model transformations nor bounding techniques using free-weighting matrix variables are employed for dealing the cross-terms that emerge from the time derivative of the Lyapunov-Krasovskii functional; instead, they are dealt using tighter integral inequalities. The proposed analysis subsequently yields a stability condition in convex LMI framework that can be solved using standard numerical packages. For deriving robust stability conditions, two categories of system uncertainties, namely, time-varying structured and polytopic-type uncertainties, are considered. The effectiveness of the proposed stability criteria is validated through standard numerical examples.     

Simple stability criteria for systems with time-varying delays

This paper considers the problem of checking stability of linear feedback systems with time-varying but bounded delays. Simple but powerful criteria of stability are presented for both continuous-time and discrete-time systems. Using these criteria, stability can be checked in a closed loop Bode plot. This makes it easy to design the system for robustness.     

含区间时变时滞的线性不确定系统鲁棒稳定性新判据

研究一类区间时变时滞线性不确定系统的鲁棒稳定性问题.通过引入增广Lyapunov泛函,结合积分不等式方法,导出了区间时变时滞线性系统的时滞相关鲁棒稳定性新判据.与现有方法不同,该方法不涉及自由权矩阵技术和任何模型变换,减少了理论和计算上的复杂性,而且在估计Lyapunov泛函导数的上界时没有忽略某些有用项.数值算例表明,所提出的判据是有效的,具有更低的保守性.     

Improved results on stability and stabilization criteria for uncertain linear systems with time-varying delays

In this paper, the problems of stability and stabilization for linear systems with time-varying delays and norm-bounded parameter uncertainties are considered. By constructing augmented Lyapunov functionals and utilizing auxiliary function-based integral inequalities, improved delay-dependent stability and stabilization criteria for guaranteeing the asymptotic stability of the system are proposed with the framework of linear matrix inequalities. Four numerical examples are included to show that the proposed results can reduce the conservatism of stability and stabilization criteria by comparing maximum delay bounds.     

Stability criteria for linear systems with multiple time-varying delays

New delay-independent and deky-dependent stability criteria for linear systems with multiple time-varying delays are established by using the time-domain method. The results are derived based on a new-type stability theorem for general retarded dynamical systems and new analysis techniques developed in the author's previous work. Unlike some results in the literature, all of the established results do not depend on the derivative of time-varying dekys. Therefore, they are suitable for the case with very fast time-varying dekys. In addition, some remarks are also given to expkin the obtained results and to point out the limitations of the previous results in the literature.     

Small-gain stability conditions for linear systems with time-varying delays

In this paper we show that a variety of stability conditions, both existing and new, can be derived for linear systems subject to time-varying delays in a unified manner in the form of scaled small-gain conditions. From a robust control perspective, our development seeks to cast the stability problem as one of robust stability analysis, and the resulting stability conditions are also reminiscent of robust stability bounds typically found in robust control theory. The development is built on the well-known conventional robust stability analysis, requiring essentially no more than a straightforward application of the small gain theorem. The derived conditions have conceptual appeal, and they can be checked using standard robust control toolboxes.     

Less conservative stability criteria for linear systems with interval time‐varying delays

The problem of the stability of a linear system with an interval time‐varying delay is investigated. A new Lyapunov–Krasovskii functional that fully uses information about the lower bound of the time‐varying delay is constructed to derive new stability criteria. It is proved that the proposed Lyapunov–Krasovskii functional can lead to less conservative results than some existing ones. Based on the proposed Lyapunov–Krasovskii functional, two stability conditions are developed using two different methods to estimate Lyapunov–Krasovskii functional's derivative. Two numerical examples are given to illustrate that the two stability conditions are complementary and yield a larger maximum upper bound of the time‐varying delay than some existing results. Copyright © 2013 John Wiley & Sons, Ltd.     

Improved stability criteria on discrete-time systems with time-varying and distributed delays

In this paper, through constructing some novel Lyapunov-Krasovskii functional (LKF) terms and using some effective techniques, two sufficient conditions are derived to guarantee a class of discrete-time time-delay systems with distributed delay to be asymptotically and robustly stable, in which the linear fractional uncertainties are involved and the information on the time-delays is fully utilized. By employing the improved reciprocal convex technique, some important terms can be reconsidered when estimating the time difference of LKF, and the criteria can be presented in terms of linear matrix inequalities (LMIs). Especially, these derived conditions heavily depend on the information of time-delay of addressed systems. Finally, three numerical examples demonstrate that our methods can reduce the conservatism more efficiently than some existing ones.     

Improved robust stability criteria for a class of Lur'e systems with interval time-varying delays and sector-bounded nonlinearity

This paper is concerned with the absolute and robust stability for a class of neutral-type Lur'e systems with an interval time-varying delay and sector-bounded nonlinearity. By discretising the delay interval into two segmentations with an unequal width, new delay-dependent sufficient conditions for the absolute and robust stability of neutral-type Lur'e systems are proposed in terms of linear matrix inequalities (LMIs) by employing a modified Lyapunov-Krasovskii functional (LKF). These conditions reduce the conservativeness in computing the maximum allowed delay bounds (MADBs) in many cases. Finally, several standard numerical examples are presented to show the effectiveness of the proposed approach.     

Novel delay-dependent stability criteria for stochastic systems with time-varying interval delay

In this paper, the problem of the stability for a class of stochastic systems with time-varying interval delay is investigated. Through constructing a novel Lyapunov-Krasovskii functional and utilizing the information of both the lower and upper bounds of the delay, the delay-dependent sufficient criteria are derived in terms of linear matrix inequalities (LMIs). Neither model transformations nor bounding techniques for cross terms is employed, so the derived criteria are less conservative than the existing results. Meanwhile, the computational complexity of the obtained stability conditions is reduced because fewer variables are involved. Numerical examples are given to show the effectiveness and the benefits of the proposed method.     

Improved stability criteria for linear time-varying systems on time scales

ABSTRACT

In this paper, asymptotic stability problems of linear time-varying (LTV) systems on time scales are considered based on a less conservative Lyapunov inequality, whose right side is not required to be necessarily negative. It is shown that the Lyapunov inequality covers not only the corresponding trivial (continuous and discrete) ones but also nontrivial ones. Based on this inequality, some necessary and sufficient conditions for asymptotic stability, exponential stability, uniformly exponential stability of LTV systems on time scales are obtained. An example about nontrivial systems is given for illustrating the effectiveness of the proposed results.     

Robust stability criteria for uncertain stochastic neural networks of neutral-type with interval time-varying delays

This paper deals with the robust stability problem of uncertain stochastic neural networks of neutral-type with interval time-varying delays. The uncertainties under consideration are norm-bounded, and the delay is assumed to be time-varying and belongs to a given interval. By using the Lyapunov-Krasovskill functional method and the linear matrix inequality (LMI) technique, the novel stability criteria are derived in terms of LMI. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed criteria.     

Delay-dependent robust stability for uncertain linear systems with interval time-varying delay

This paper is concerned with the delay-dependent robust stability problem for uncertain linear systems with interval time-varying delay. The time-varying delay is assumed to belong to an interval and no restriction on the derivative of the time-varying delay is needed, which allows the delay to be a fast time-varying function. The uncertainty under consideration is norm-bounded, and possibly time-varying, uncertainty. Based on the Lyapunov-Krasovskii functional approach, a stability criterion is derived by introducing some relaxation matrices that can be used to reduce the conservatism of the criteria. Numerical examples are given to demonstrate effectiveness of the proposed method.     

Exponential stability of linear distributed parameter systems with time-varying delays

Exponential stability analysis via the Lyapunov-Krasovskii method is extended to linear time-delay systems in a Hilbert space. The operator acting on the delayed state is supposed to be bounded. The system delay is admitted to be unknown and time-varying with an a priori given upper bound on the delay. Sufficient delay-dependent conditions for exponential stability are derived in the form of Linear Operator Inequalities (LOIs), where the decision variables are operators in the Hilbert space. Being applied to a heat equation and to a wave equation, these conditions are reduced to standard Linear Matrix Inequalities (LMIs). The proposed method is expected to provide effective tools for stability analysis and control synthesis of distributed parameter systems.     

一类区间时变时滞系统的稳定性分析

针对一类区间时变时滞系统的稳定性问题,进行了全局渐近稳定性分析.通过引入时滞分段方法和构建恰当的Lyapunov-Krasovskii泛函,得到了新的区间时滞相关稳定性判定准则.该准则以线性矩阵不等式形式给出,便于利用LMI工具箱对系统的稳定性进行判定.新准则具有较少的保守性,并且在一定范围内保守性随着时滞分段增多而减少,即时滞分段越多,保守性越少.数值仿真算结果例表明了新准则所具有的有效性和较少的保守性.