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.     

An improved LMI-based approach for stability of piecewise affine time-delay systems with uncertainty

The stability problem for uncertain piecewise affine (PWA) time-delay systems is investigated in this article. It is assumed that there exists a known constant time delay in the system and the uncertainly is norm-bounded. Sufficient conditions for the stability of nominal systems and the stability of systems subject to uncertainty are derived using the Lyapunov–Krasovskii functional with a triple integration term. This approach handles switching based on the delayed states (in addition to the states) for a PWA time-delay system, considers structured as well as unstructured uncertainty and reduces the conservativeness of previous approaches. The effectiveness of the proposed approach is demonstrated by comparing with the existing methods through numerical examples.     

Robust analysis and synthesis of linear time-delay systems with norm-bounded time-varying uncertainty

The problems of robust analysis and synthesis of systems with state-delay and norm-bounded time-varying parameter uncertainty are studied. It is shown that these problems are equivalent to the H_∞ analysis and synthesis problems of an auxiliary system, which is independent of the time-delay and the uncertainty in the system. The necessary and sufficient conditions for the equivalence are developed. Thus any standard H_∞ analysis and synthesis method can be used to solve this problem.     

Robust Hinfinity state feedback control of discrete time-delay linear systems with norm-bounded uncertainty

This paper studies, via a linear matrix inequality approach, the problem of Hinfinity control for discrete time-delay linear systems with parametric uncertainty. The system under consideration is subjected to both time-varying norm-bounded parameter uncertainty and time delay in the state. First, the problem of robust stability of the underlying system is investigated. Next, we address the problem of robust Hinfinity state feedback control in which both robust stability and a prescribed Hinfinity performance are required to be achieved irrespective of the uncertainty and time delay. It is shown that the above problem can be solved if a linear matrix inequality has a symmetric positive definite solution.     

On robust stability of time-delay systems with norm-boundeduncertainty

This paper considers the robust stability problem for a class of time-delay systems with norm-bounded, and possibly time-varying uncertainty. Based on the discretized Lyapunov functional approach, a stability criterion is derived. The time-delay is assumed constant and known. Numerical examples show that the results obtained by this new criterion significantly improve the estimate of the stability limit over some existing results in the literature     

带有时滞的区间动力系统的鲁棒稳定性研究

给出了区间动力系统稳定性的相关概念,讨论了带有时滞的区间动力系统的鲁棒稳定性.通过构造控制矩阵和迭代相结合的方法,给出了一类带有时滞的区间动力系统鲁棒稳定的判别方法,并且给出了系统鲁棒稳定时参数取值的最大区间.将含有时滞的区间动力系统的稳定性转化为判别一个矩阵的稳定性,推广和改进了已有的结论.     

具有时滞的线性区间动力系统的鲁棒稳定性

利用Lyapunov原理,给出了具有时滞的线性区间动力系统鲁棒稳定的一些充分条件,推广和改进了前人关于具有时滞的线性区间动力系统的鲁棒稳定性的相关结论,并举例说明了本文结果不仅保守性小,且计算简单.     

时变不确定离散时滞系统的H∞鲁棒控制

研究了一类线性不确定离散时滞系统的H∞鲁棒控制问题,其时变不确定项是范数有界的,但无需满足匹配条件.基于线性矩阵不等式(LMI)方法,得到了可H∞鲁棒镇定的一个充分条件.通过求解一个特定的线性矩阵不等式,即可获得H∞状态反馈控制器.具体算例说明了该方法的有效性.     

不确定时滞系统的鲁棒绝对稳定性研究

基于Lyapunov稳定性理论，采用线性矩阵不等式处理方法，研究具有参数不确定性的时滞系统鲁棒绝对稳定性问题．导出了用线性矩阵不等式系统可行性描述的系统鲁棒绝对稳定的滞后依赖型条件，据此可计算出最大的允许时滞界．通过求解一组线性矩阵不等式，给出使得闭环系统鲁棒绝对稳定的无记忆状态反馈控制律设计方法。     

An improved approach to delay-dependent robust stabilization for uncertain singular time-delay systems

In this paper, delay-dependent stability analysis and robust stabilization for uncertain singular time-delay systems are addressed. By using Jensen integral inequality, an improved delay-dependent criterion of admissibility for singular time-delay systems is proposed in terms of linear matrix inequality (LMI). Our new proposed criterion is less conservative and the numerical complexity is smaller than the existing ones. Based on this criterion, a state feedback controller is designed to ensure that the uncertain singular time-delay system is admissible. Finally, three numerical examples are employed to illustrate the effectiveness of the proposed method.