一类含时变分布时滞的退化中立型系统的鲁棒稳定性(英文)

考虑含分布时滞的退化中立型系统的鲁棒稳定性.利用算子Ω的稳定性和线性矩阵不等式得到一个新的鲁棒稳定性判据,本判据将中立型时滞、时变离散时滞、时变分布时滞和退化中立型系统一起考虑,相比已有文献具有较低的保守性.利用Matlab可以验证本判据的有效性.     

Exponential stability and applications of switched positive linear impulsive systems with time-varying delays and all unstable subsystems

The global uniform exponential stability of switched positive linear impulsive systems with time-varying delays and all unstable subsystems is studied in this paper, which includes two types of distributed time-varying delays and discrete time-varying delays. Switching behaviors dominating the switched systems can be either stabilizing and destabilizing in the new designed switching sequence. We design new linear programming algorithm process to find the feasible ratio of stabilizing switching behaviors, which can be compensated by unstable subsystems, destabilizing switching behaviors, and impulses. Specically, we add a kind of nonnegative impulses which is consistent with the switching behaviors for the systems. Employing a multiple co-positive Lyapunov-Krasovskii functional, we present several new sufficient stability criteria and design new switching sequence. Then, we apply the obtained stability criteria to the exponential consensus of linear delayed multi-agent systems, and obtain the new exponential consensus criteria. Three simulations are provided to demonstrate the proposed stability criteria.     

具变时滞的非线性退化微分系统的渐近稳定性判据

In this paper, the asymptotic stability for singular differential nonlinear systems with multiple time-varying delays is considered. The V-functional method for general singular differential delay system is investigated. The asymptotic stability criteria for singular differential nonlinear systems with multiple time-varying delays are derived based on V-functional method and some analytical techniques, which are described as matrix equations or matrix inequalities. The results obtained are computationally flexible and efficient.     

The Algebraic Criteria for the All-delay Stabilityof Two-dim ensional Degenerate Differential System swith Delay

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＡｓｔｈｅｄｅｅｐｌｙｄｅｖｅｌｏｐｍｅｎｔｏｆｔｈｅｓｔｕｄｙａｎｄａｐｐｌｉｃａｔｉｏｎｆｏｒｍａｎｙｐｒａｃｔｉｃａｌｓｙｓｔｅｍｓ，ｓｕｃｈａｓｅｃｏｎｏｍｉｃｍａｎａｇｅｍｅｎｔｓｙｓｔｅｍｓ，ｅｎｇｉｎｅｅｒｉｎｇｓｙｓｔｅｍｓ，ｐｏｗｅｒｓｙｓｔｅｍｓａｎｄｓｏｏｎ，ｐｅｏｐｌｅｄｅｖｏｔｅｍｕｃｈａｎｄｍｕｃｈａｔｔｅｎｔｉｏｎｔｏｔｈｅｐｈｅｎｏｍｅｎａｏｆｄｅｌａｙｓ［１］［２］．Ａｔｔｈｅｓａｍｅｔｉｍｅ，ｐｅｏｐｌｅｆｏｕｎｄｔｈａｔｔｈｅ…     

Exponential stability results for uncertain neutral systems with interval time-varying delays and Markovian jumping parameters

This paper deals with the global exponential stability analysis of neutral systems with Markovian jumping parameters and interval time-varying delays. The time-varying delay is assumed to belong to an interval, which means that the lower and upper bounds of interval time-varying delays are available. A new global exponential stability condition is derived in terms of linear matrix inequality (LMI) by constructing new Lyapunov-Krasovskii functionals via generalized eigenvalue problems (GEVPs). The stability criteria are formulated in the form of LMIs, which can be easily checked in practice by Matlab LMI control toolbox. Two numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.     

Improved stability criteria for neutral type Lur’e systems with time-varying delays

In this letter, the problem of stability analysis for neutral type Lur’e systems with interval time-varying delays is considered. By introducing a novel Lyapunov–Krasovskii (L–K) functional and utilizing second order reciprocal convex combination technique and Finsler lemma, an improved delay-dependent stability criteria is derived in terms of linear matrix inequalities (LMIs). The information about the time-varying delays and their upper bounds are fully used in the L–K functional. Finally, a numerical example is provided to illustrate the effectiveness of the proposed method.     

Improved delay-dependent robust stability criteria for a class of uncertain mixed neutral and Lur’e dynamical systems with interval time-varying delays and sector-bounded nonlinearity

The previously proposed delay-dependent robust stability criteria for a class of uncertain mixed neutral and Lur’e dynamical systems with interval time-varying delays are refined by eliminating nonlinearity and/or reducing the number of free-weighting matrices. Several robust stability criteria proposed in this paper are simpler and effective. Numerical examples show that the new method is less conservative than some previous approaches.     

On exponential stability of nonlinear differential systems with time-varying delay

General nonlinear differential systems with time-varying delays are considered. Several explicit criteria for exponential stability are presented. An example is given to illustrate the obtained results. To the best of our knowledge, the results of this note are new.     

不确定变时滞系统的一个时滞相关稳定性判据

本文讨论不确定变时滞系统的稳定性问题.基于一个新的Lyapunov泛函,并利用一种新的方法处理不确定项,得到了不确定变时滞系统的一个时滞相关的稳定性判据,并利用矩阵不等式的形式给出该判据.与已有文献相比较,所得结论允许时滞导数(?)(t)(?)1且具有较少的限制条件,因此具有较弱的保守性.最后,通过两个例子验证了所给结论的正确性.     

A novel approach on stabilization for linear systems with time-varying input delay

This paper presents new results on delay-dependent stability and stabilization for linear systems with interval time-varying delays. Some less conservative delay-dependent criteria for determining the stability of the time-delay systems are obtained in this paper. Based on the stability conditions, we propose a new state transformation technology to facilitate controller designing efficiently and computationally. The method is also applicable to the existing stability conditions reported by now, while the existing technologies may fail to derive computational control procedures from the stability conditions. Finally, some numerical examples well illustrate the effectiveness of the proposed method.     

Linear Matrix Inequality Approach to New Delay-Dependent Stability Criteria for Uncertain Dynamic Systems with Time-Varying Delays

In this paper, the problem of delay-dependent stability for uncertain dynamic systems with time-varying delays is considered. The parameter uncertainties are assumed to be norm-bounded. Using a new augmented Lyapunov functional, novel delay-dependent stability criteria for such systems are established in terms of LMIs (linear matrix inequalities), which can be solved easily by the application of convex optimization algorithms. Three numerical examples are given to show the superiority of the proposed method.     

A new augmented Lyapunov-Krasovskii functional approach for stability of linear systems with time-varying delays

This paper proposes improved delay-dependent conditions for asymptotic stability of linear systems with time-varying delays. The proposed method employs a suitable Lyapunov-Krasovskii’s functional for new augmented system. Based on Lyapunov method, delay-dependent stability criteria for the systems are established in terms of linear matrix inequalities (LMIs) which can be easily solved by various optimization algorithms. Three numerical examples are included to show that the proposed method is effective and can provide less conservative results.     

Global exponential stability of impulsive discrete-time neural networks with time-varying delays

This paper studies the problem of global exponential stability and exponential convergence rate for a class of impulsive discrete-time neural networks with time-varying delays. Firstly, by means of the Lyapunov stability theory, some inequality analysis techniques and a discrete-time Halanay-type inequality technique, sufficient conditions for ensuring global exponential stability of discrete-time neural networks are derived, and the estimated exponential convergence rate is provided as well. The obtained results are then applied to derive global exponential stability criteria and exponential convergence rate of impulsive discrete-time neural networks with time-varying delays. Finally, numerical examples are provided to illustrate the effectiveness and usefulness of the obtained criteria.     

Stability analysis for neutral systems with mixed delays

Relationships between system states contained in the neutral equation are used to address the delay-dependent stability of a neutral system with time-varying state delay. Using linear matrix inequalities, we present a new asymptotic stability criterion, and a new robust stability criterion, for neutral systems with mixed delays. Since the criteria take into account the sizes of the neutral delay, discrete delay and the derivative of discrete delay, they are less conservative than those produced by previous approaches. Numerical examples are presented to demonstrate that these criteria are indeed more effective.     

New robust stability criteria for uncertain neural networks with interval time-varying delays

In this paper, problem of robust stability of uncertain neural networks with interval time-varying delays has been investigated. The delay factor is assumed to be time-varying and belongs to a given interval, which means that the lower and upper bounds of the interval time-varying delays are available. Based on the Lyapunov–Krasovskii functional approach, a new delay-dependent stability criteria is presented in terms of linear matrix inequalities (LMIs). Two numerical examples are given to illustrate the effectiveness of the proposed method.     

Robust stability analysis of stochastic delayed genetic regulatory networks with polytopic uncertainties and linear fractional parametric uncertainties

This study examines the problem of robust stability of uncertain stochastic genetic regulatory networks with time-varying delays. The system’s uncertainties are modeled as both polytopic form and structured linear fractional form. Based on a novel augmented Lyapunov–Krasovskii functional and different integral approaches, new stability conditions have been derived. Furthermore, these stability criteria can be applicable to both fast and slow time-varying delays. Finally, a numerical example is presented to illustrate the effectiveness of the proposed stability conditions.     

Decentralized Stabilizing State Feedback Controllers for a Class of Large-Scale Systems Including State Delays in the Interconnections

The problem of the decentralized stabilization of a class of large-scale nonlinear and linear systems including time-varying delays in the interconnections is considered. By combining the Razumikhin-type theorem with the Lyapunov stability theory, we propose a class of decentralized state feedback controllers which can guarantee always some type of stability of large-scale time-delay systems. In this paper, we assume that the time-varying delays are continuous and bounded nonnegative functions. Furthermore, since the proposed decentralized state feedback controllers are independent of the delays, the results obtained in this paper are applicable to systems without exact knowledge of the delays, i.e., systems with perturbed delays. Finally, a numerical example is given to demonstrate the validity of the results.     

Improved results on robust exponential stability criteria for neutral-type delayed neural networks

In this paper, we investigate the problem of robust global exponential stability analysis for a class of neutral-type neural networks. The interval time-varying delays allow for both slow and fast time-varying delays. The values of the time-varying uncertain parameters are assumed to be bounded within given compact sets. Improved global exponential stability condition is derived by employing new Lyapunov-Krasovskii functional and the integral inequality. The developed nominal and robust stability criteria is delay-dependent and characterized by linear-matrix inequalities (LMIs). The developed results are less conservative than previous published ones in the literature, which are illustrated by representative numerical examples.