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.     

On robust stability of neutral systems with time-varying discrete delay and norm-bounded uncertainty

This paper investigates the robust stability of uncertain linear neutral systems with time-varying discrete delay. A delay-dependent stability criterion is obtained and formulated in the form of a linear matrix inequality. Two numerical examples are given to indicate significant improvements over some existing results.     

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.     

Delay-range-dependent stability for systems with time-varying delay

This paper is concerned with the stability analysis for systems with time-varying delay in a range. An appropriate type of Lyapunov functionals is proposed to investigate the delay-range-dependent stability problem. The present results may improve the existing ones due to a method to estimate the upper bound of the derivative of Lyapunov functional without ignoring some useful terms and the introduction of additional terms into the proposed Lyapunov functional, which take into account the range of delay. Numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method.     

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-dependent criteria for robust stability of time-varying delay systems

This paper deals with the problem of delay-dependent robust stability for systems with time-varying structured uncertainties and time-varying delays. Some new delay-dependent stability criteria are devised by taking the relationship between the terms in the Leibniz-Newton formula into account. Since free weighting matrices are used to express this relationship and since appropriate ones are selected by means of linear matrix inequalities, the new criteria are less conservative than existing ones. Numerical examples suggest that the proposed criteria are effective and are an improvement over previous ones.     

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.     

Improved robust stability criteria for uncertain systems with time‐varying delay

This paper is concerned with the delay‐dependent stability and robust stability for uncertain systems with time‐varying delay. Through constructing an appropriate type of Lyapunov‐Krasovskii functional and proving its positive definiteness, using slack matrices and a convex combination condition, the delay‐dependent stability criteria, which are less conservative, are derived in terms of linear matrix inequalities. Numerical examples are also given to illustrate the improvement on the conservatism of the delay bound over some existing results. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Delay-dependent criteria for the robust stability of systems with time-varying delay

The problem of delay-dependent robust stability for systems with time-varying delay has been considered. By using the S-procedure and the Park's inequality in the recent issue, a delay-dependent robust stability criterion which is less conservative than the previous results has been derived for time-delay systems with time-varying structured uncertainties. The same idea has also been easily extended to the systems with nonlinear perturbations. Numerical examples illustrated the effectiveness and the improvement of the proposed approach.     

Observer-based robust stabilization for uncertain systems with unknown time-varying delay

This paper focuses on the problem of robust stabilization for a class of linear systems with uncertain parameters and time varying delays in states. The parameter uncertainty is continuous, time varying, and norm-bounded. The state delay is unknown and time varying. The states of the system are not all measurable and an observer is constructed to estimate the states. If a linear matrix inequality (LMI) is solvable, the gains of the controller and observer can be obtained from the solution of the LMI. The observer and controller are dependent on the size of time delay and on the size of delay derivative. Finally, an example is given to illustrate the effectiveness of the proposed control method.     

Delay-range-dependent robust stabilization for uncertain T-S fuzzy control systems with interval time-varying delays

This paper is concerned with robust stabilization for a class of T-S fuzzy control systems with interval time-varying delays. An approach is proposed to significantly improve the system performance while reducing the number of scalar decision variables in linear matrix inequalities. The main points of the approach are: (i) two coupling integral inequalities are proposed to deal with some integral items in the derivation of the stability criteria; (ii) an appropriate Lyapunov-Krasovskii functional is constructed by including both the lower and upper bounds of the interval time-varying delays; and (iii) neither model transformation nor free weighting matrices are employed in the theoretical result derivation. As a result, some improved sufficient stability criteria are derived, and the maximum allowable delay bound and controller gains can be obtained simultaneously by solving an optimization problem. Numerical examples are given to demonstrate the effectiveness of the proposed approach.     

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.     

Stability analysis of systems with time-varying delay via relaxed integral inequalities

This paper investigates the stability of linear systems with a time-varying delay. The key problem concerned is how to effectively estimate single integral term with time-varying delay information appearing in the derivative of Lyapunov–Krasovskii functional. Two novel integral inequalities are developed in this paper for this estimation task. Compared with the frequently used inequalities based on the combination of Wirtinger-based inequality (or Auxiliary function-based inequality) and reciprocally convex lemma, the proposed ones can provide smaller bounding gap without requiring any extra slack matrix. Four stability criteria are established by applying those inequalities. Based on three numerical examples, the advantages of the proposed inequalities are illustrated through the comparison of maximal admissible delay bounds provided by different criteria.     

Delay-dependent robust stabilisation of uncertain discrete-time switched systems with time-varying state delay

This paper considers the stabilisation problem for uncertain discrete-time switched systems with time-varying delay in the state. The uncertainty is assumed to be of structured linear fractional form, which includes the norm-bounded uncertainty as a special case. A stability condition is first proposed by using switched Lyapunov function, which is dependent on the minimum and maximum delay bounds. Based on the result, a switched state feedback controller is designed. Numerical examples are given to illustrate the effectiveness of the result.     

一类时变时滞系统的稳定性分析

针对时变时滞系统稳定性问题, 在考虑非线性扰动的情况下, 为了降低时变时滞系统稳定性判据的保守性, 以改进的Jensen 不等式, Wirtinger型双重积分不等式以及优化凸组合技术为基础, 构造增广的Lyapunov-Krasovskii 泛函, 得到了新的时滞相关稳定性判据. 最后, 通过数值仿真对比可知, 该稳定性判据具有较小的保守性和良好的鲁棒性.     

Delay-dependent stability analysis for discrete-time singular Markovian jump systems with time-varying delay

This article considers the problem of delay-dependent stability analysis for a class of discrete-time singular systems with Markovian jump and time-varying delay. The transition probabilities in Markov chain are assumed to be partially unknown. In terms of linear matrix inequality approach, the delay-dependent criteria are proposed to ensure the underlying system to be regular, causal and stochastically stable. Several numerical examples are given to demonstrate the effectiveness and less conservatism of the obtained results.     

New stability criteria of singular systems with time-varying delay via free-matrix-based integral inequality

This paper concerns the stability problem of singular systems with time-varying delay. First, the singular system with time-varying delay is transformed into the neutral system with time-varying delay. Second, a more proper Lyapunov–Krasovskii functional (LKF) is constructed by adding some integral terms to quadratic forms. Then, to obtain less conservative conditions, the free-matrix-based integral inequality is adopted to estimate the derivative of LKF. As a result, some delay-dependent stability criteria are given in terms of linear matrix inequalities. Finally, two numerical examples are provided to demonstrate the effectiveness and superiority of the proposed method.     

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.     

多时变时滞系统的鲁棒稳定及有界实引理的时滞相关条件

对于多时变时滞系统,引入表示牛顿-莱布尼兹公式中各项的相互关系的自由权矩阵,获得了基于线性矩阵不等式(LMI)描述的系统鲁棒稳定的时滞相关条件,并说明了时滞相关条件和时滞无关条件的相互关系.在此基础上,将其推广到有界实引理的时滞相关条件.所得结果克服了已有结果的保守性.最后给出实例说明本文方法的有效性.     

An augmented model for robust stability analysis of time-varying delay systems

Stability analysis of linear systems with time-varying delay is investigated. In order to highlight the relations between the variation of the delay and the states, redundant equations are introduced to construct a new modelling of the delay system. New types of Lyapunov–Krasovskii functionals are then proposed allowing to reduce the conservatism of the stability criterion. Delay-dependent stability conditions are then formulated in terms of linear matrix inequalities. Finally, several examples show the effectiveness of the proposed methodology.