Robust Stability and Stabilization of Discrete Singular Systems with Interval Time-varying Delay and Linear Fractional Uncertainty

The robust stability and robust stabilization problems for discrete singular systems with interval time-varying delay and linear fractional uncertainty are discussed. A new delay-dependent criterion is established for the nominal discrete singular delay systems to be regular, causal and stable by employing the linear matrix inequality （LMI） approach. It is shown that the newly proposed criterion can provide less conservative results than some existing ones. Then, with this criterion, the problems of robust stability and robust stabilization for uncertain discrete singular delay systems are solved, and the delay-dependent LMI conditions are obtained. Finally, numerical examples are given to illustrate the effectiveness of the proposed approach.

Robust Stability Criteria for Neutral Systems with Interval Time-Varying Delays and Nonlinear Perturbations

This paper investigates the problem of delay-dependent robust stability analysis for a class of neutral systems with interval time-varying delays and nonlinear perturbations. Such nonlinear perturbations are with time-varying but norm-bounded characteristics. Based on a new Lyapunov-Krasovskii functional together with a free-weighting matrices technique,improved delay-dependent stability criteria are established. It is shown that less conservative results can be obtained in terms of linear matrix inequalities( LMIs). Numerical examples are provided to demonstrate the effectiveness and less conservatism of the proposed approach.

Further Results on Delay-distribution-dependent Robust Stability Criteria for Delayed Systems

This paper concerns the robust stability analysis of uncertain systems with time delays as random variables drawn from some probability distribution. The delay-distribution-dependent criteria for the exponential stability of the original system in mean square sense are achieved by Lyapunov functional method and the linear matrix inequality （LMI） technique. The proposed approach involves neither free weighting matrices nor any model transformation, and it shows that the new criteria can provide less conservative results than some existing ones. Numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method.

Improved delay-dependent robust H_∞ control of an uncertain stochastic system with interval time-varying and distributed delays

In this paper, the robust H∞control problem for a class of stochastic systems with interval time-varying and distributed delays is discussed. The system under study involves parameter uncertainty, stochastic disturbance, interval time-varying,and distributed delay. The aim is to design a delay-dependent robust H∞control which ensures the robust asymptotic stability of the given system and to express it in the form of linear matrix inequalities（LMIs）. Numerical examples are given to demonstrate the effectiveness of the proposed method. The results are also compared with the existing results to show its conservativeness.

Delay-dependent exponential stability of impulsive stochastic systems with time-varying delay

The problem of delay-dependent exponential stability is investigated for impulsive stochastic systems with time-varying delay. Although the exponential stability of impulsive stochastic delay systems has been discussed by several authors, few works have been done on delay-dependent exponential stability of impulsive stochastic delay systems. Firstly, the Lyapunov-Krasovskii functional method combing the free-weighting matrix approach is applied to investigate this problem. Some delay-dependent mean square exponential stability criteria are derived in terms of linear matrix inequalities. In particular, the estimate of the exponential convergence rate is also provided, which depends on system parameters and impulsive effects. The obtained results show that the system will stable if the impulses＇ frequency and amplitude are suitably related to the increase or decrease of the continuous flows, and impulses may be used as controllers to stabilize the underlying stochastic system. Numerical examples are given to show the effectiveness of the results.

Delay Dependent Robust Stability of Singular Systems with Additive Time-varying Delays

This paper considers the problem of delay-dependent robust stability for uncertain singular systems with additive time-varying delays. The purpose of the robust stability problem is to give conditions such that the uncertain singular system is regular, impulse free, and stable for all admissible uncertainties. The results are expressed in terms of linear matrix inequalities （LMIs）. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed method.

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.

New Robust Exponential Stability Analysis for Uncertain Neural Networks with Time-varying Delay

In this paper,the global robust exponential stability is considered for a class of neural networks with parametric uncer- tainties and time-varying delay.By using Lyapunov functional method,and by resorting to the new technique for estimating the upper bound of the derivative of the Lyapunov functional,some less conservative exponential stability criteria are derived in terms of linear matrix inequalities (LMIs).Numerical examples are presented to show the effectiveness of the proposed method.

Delay-dependent Robust Stabilization and H_∞ Control for Uncertain Stochastic T-S Fuzzy Systems with Discrete Interval and Distributed Time-varying Delays

In this paper, delay-dependent robust stabilization and H∞ control for uncertain stochastic Takagi-Sugeno （T-S） fuzzy systems with discrete interval and distributed time-varying delays are discussed. The purpose of the robust stochastic stabilization problem is to design a memoryless state feedback controller such that the closed-loop system is mean-square asymptotically stable for all admissible uncertainties. In the robust H∞ control problem, in addition to the mean-square asymptotic stability requirement, a prescribed H∞ performance is required to be achieved. Sufficient conditions for the solvability of these problems are proposed in terms of a set of linear matrix inequalities （LMIs） and solving these LMIs, a desired controller can be obtained. Finally, two numerical examples are given to illustrate the effectiveness and less conservativeness of our results over the existing ones.

具概率分布变时滞随机系统鲁棒稳定性

本文研究了一类有非线性时变随机时滞的线性不确定系统的鲁棒稳定性.其中时变随机时滞表征为伯努利随机过程,具有已知的概率分布和变化范围.通过构造新泛函,建立了基于线性矩阵不等式的鲁棒均方指数稳定的充分条件,此条件易于用MATLAB工具箱来验证.本文所获得结果的主要特征是稳定性条件依赖时滞的概率分布和时滞导数的上界.同时也证明了允许时变随机时滞的时滞比之传统的确定性时滞有更大的变化范围,因此我们的条件比确定性时滞更为保守.算例表明了文中所提方法的有效性.

不确定中立型随机时滞系统的鲁棒随机稳定性

研究了一类不确定中立型随机时滞系统的鲁棒随机稳定性。利用Lyapunov泛函方法,得到了基于线性矩阵不等式表示的几个稳定性充分性判据。数值模拟实例说明了本文所得结论的有效性。