混合变时滞不确定中立型系统鲁棒稳定性分析

研究一类含混合变时滞不确定中立系统时滞相关鲁棒稳定性问题。基于时滞中点值,把时滞区间均分成两部分,通过构造包含时滞中点信息的增广泛函和三重积分项的Lyapunov-Krasovskii (L-K)泛函,利用L-K稳定性定理、积分不等式方法和自由权矩阵技术,建立了一种基于线性矩阵不等式(LMI)的、与离散时滞和中立时滞均相关的鲁棒稳定性判据。数值算例表明,该判据改善了已有文献的结论,具有更低的保守性。     

Stability analysis of fuzzy large-scale systems with time delays in interconnections

The stability problem of fuzzy large-scale systems with time delays in interconnections is considered in this paper. The fuzzy large-scale system consists of J interconnected subsystems, which are represented by Takagi-Sugeno (T-S) fuzzy models. The stability conditions are derived using the Lyapunov-Krasovskii functional approach. This condition is independent of time delay and does not need the solution of a Lyapunov equation or Riccati equation. A stabilization approach for the delayed fuzzy large-scale systems through fuzzy state feedback-based controller is also presented in this paper. Finally, an example is given to demonstrate the result.     

Stability analysis of neutral systems with distributed delays

The stability of neutral systems with distributed delays is investigated in this paper. A modified Lyapunov-Krasovskii functional is constructed to study this class of systems. The proposed stability criterion is discrete-, distributed- and neutral-delay-dependent. In addition, by this method one can study the case when the coefficient matrix of the neutral delay term is time-varying uncertain. The reduced conservatism is illustrated in a numerical example.     

Stability problem of systems with multiple delay channels

A new form of coupled differential-difference equations with one delay in each channel is proposed to model systems with multiple delays. This formulation has significant advantage over the traditional differential-difference equations or the prevailing form of coupled differential-difference equations with multiple delays. Fundamental solutions, general solutions, and the construction of the Lyapunov-Krasovskii functional are discussed. For systems with a large number of state variables with multiple low-dimensional delay elements, this formulation allows a drastic reduction of computational cost as compared to the traditional differential-difference equation formulation when the discretized Lyapunov-Krasovskii functional method is used.     

On stability of linear neutral systems with mixed time delays: A discretized Lyapunov functional approach

This paper focuses on the stability problem for a class of linear neutral systems with mixed neutral and discrete delays. A discretized Lyapunov functional approach is developed for such kinds of systems. The resulting stability criteria are formulated in the form of a linear matrix inequality (LMI). These criteria are applicable to linear neutral systems with both small and non-small discrete delays. For nominal systems, the analytical results can be approached with fine discretization. For uncertain systems, the new approach is much less conservative. Numerical examples show significant improvement over approaches in the literature.     

Lyapunov-Krasovskii functional for uniform stability of coupled differential-functional equations

This article discusses the Lyapunov-Krasovskii functional approach for the stability problem of coupled differential-functional equations. Such systems include, as special cases, many types of time-delay systems, including the lossless propagation model, some neutral time-delay systems and singular time-delay systems. After the general stability theory, the special case of coupled differential-difference equations is discussed, and the necessity for the existence of quadratic Lyapunov-Krasovskii functional is established. Discretization is used to render the stability criterion to an LMI form.     

Stability analysis of systems with stochastically varying delays

A stability analysis of linear systems with stochastically varying delay is performed. It is assumed that the delay function has the form of a sawtooth with switches occurring at the arrival times of a homogeneous Poisson process. Several notions of stochastic stability are considered and corresponding stability criteria are derived. For two examples the different criteria are compared and the effect on stability of various deterministic approximations is examined.     

Robust stability for uncertain neutral systems with mixed time-varying delays

The robust stability of uncertain neutral systems with mixed time-varying delays is investigated in this paper. The uncertainties under consideration are norm-bounded and time-varying. Based on the Lyapunov stability theory, a delay-dependent stability criterion is derived and given in the form of a linear matrix inequality （LMI）. Finally, a numerical example is given to illustrate significant improvement over some existing results.     

带有混合时滞的切换系统的耗散性分析与控制

本文研究了一类具有不稳定子系统和混合时滞的切换系统的耗散性和指数镇定问题. 首先, 为了消除不稳 定子系统给这类时滞系统带来的不利影响, 采用了一种新颖的切换信号设计方法–将模态依赖平均驻留时间的慢切 换和快切换方法相结合, 并通过利用Lyapunov相关理论, 给出了全局指数稳定的充分条件. 然后, 利用耗散性理 论、多重Lyapunov-Krasovskii泛函技术、积分不等式、与Schur补引理等方法, 以线性矩阵不等式的形式给出了耗散 性能的相关判据, 使闭环系统实现全局指数稳定性的同时具有严格耗散性能. 进一步, 在给定扰动衰减水平的前提 下, 通过求解一些严格的LMI条件, 建立了一组可行控制器. 最后, 通过仿真实例验证了该方法的有效性.     

A descriptor system approach to robust stability of uncertain neutral systems with discrete and distributed delays

The robust stability of uncertain linear neutral systems with discrete and distributed delays is investigated. The uncertainties under consideration are norm bounded, and possibly time varying. The proposed stability criteria are formulated in the form of a linear matrix inequality and it is easy to check the robust stability of the considered systems. Numerical examples are given to indicate significant improvements over some existing results.     

时滞系统稳定性分析:一种积分等式方法

提出一种积分等式方法研究时滞系统稳定性问题.该方法是已有积分不等式方法的改进.结合自由权矩阵构建积分等式,且自由权矩阵的选取由Lyapunov-Krasovskii泛函的导数确定,从而在稳定条件的推导过程中,不引入任何模型转换及限界方法.基于该方法,可得到具有更低保守性的稳定条件.仿真例子说明了所提方法的有效性.     

带有非线性扰动的时变时滞系统的稳定性准则

研究了带有非线性扰动的时变时滞系统的稳定性问题.基于时滞分割方法,提出了保守性更小的系统稳定性分析准则.利用一个自由参数将时滞区间分割为2个子区间,进而构造了含有时滞分割点状态信息和3重积分项的Lyapunov-Krasovskii泛函,并采用自由矩阵积分不等式界定泛函导数中的交叉项.基于Lyapunov稳定性定理,得到了以线性矩阵不等式描述的时滞相关型稳定性准则.数值算例表明该稳定性准则能够得到更大的时滞上界,与已有结果相比具有更小的保守性.     

Stability analysis of systems with aperiodic sample-and-hold devices

Motivated by the widespread use of networked and embedded control systems, improved stability conditions are derived for sampled-data feedback control systems with uncertainly time-varying sampling intervals. The results are derived by exploiting the passivity-type property of the operator arising in the input-delay approach to the system in addition to the gain of the operator, and are hence less conservative than existing ones.     

Stability analysis of large-scale systems with delays

New sufficient conditions for delay-independent asymptotic stability of large-scale systems are presented by using the properties of matrix norm and measure. The proposed method is simple and effective.     

Stability and dissipativity analysis for uncertain Markovian jump systems with random delays via new approach

This paper studies the problem of stability and dissipativity analysis for uncertain Markovian jump systems (UMJSs) with random time-varying delays. Based on the auxiliary function-based integral inequality (AFBII) and with the help of some mathematical tools, a new double integral inequality (NDII) is developed. Then, to show the efficiency of the proposed inequality, a suitable Lyapunov-Krasovskii functional (LKF) is constructed with augmented delay-dependent terms. By employing integral inequalities, new delay-dependent sufficient conditions are derived in terms of linear matrix inequalities (LMIs). Finally, illustrative examples are given to show the effectiveness and less conservatism of the results.     

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.     

Delay-dependent robust stability of uncertain fuzzy large-scale systems with time-varying delays

This paper addresses the stability problem of fuzzy large-scale systems (FLSSs) with uncertainties and arbitrary time-varying delays. The stability conditions, which are less conservative and more applicable than the existing results, are derived by a novel Lyapunov-Krasovskii functional method and expressed in terms of linear matrix inequalities (LMIs). Two examples are given to demonstrate the correctness and advantage of our theoretical results.     

混合时滞不确定中立系统鲁棒稳定的时滞分割方法

研究了一类同时具有离散与分布时滞的不确定中市型系统的鲁棒稳定性问题.基于时滞分割思想,通过构造一类特殊的Lyapunov-Krasovskii泛函,并利用Jensen不等式,建立了线性矩阵不等式形式的时滞相关鲁棒稳定性新判据.该方法不涉及模型变换与自由权矩阵技术,减少了理论与计算上的复杂性;同时允许中立时滞项的系数矩阵...     

Linear quadratic suboptimal control for time delays systems

A simple method is developed for determining an output feedback matrix which places m+l—?1 poles of a linear multivariate system at any specified locations, where m and l are the input and output dimensions respectively. The feedback matrix is constructed as the sum of two unity rank matrices. The first places m— 1 poles and the second, while preserving these m— 1 poles, places I additional poles. A numerical example is given for illustration.