Delay-dependent non-fragile robust stabilization and H∞ control of uncertain stochastic systems with time-varying delay and nonlinearity
Delay-dependent non-fragile robust stabilization and H∞ control of uncertain stochastic systems with time-varying delay and nonlinearity
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DOI：
10.1016/j.jfranklin.2011.06.010
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发表时间：
2011-10
期刊：
影响因子：
--
通讯作者：
Cheng Wang;Yi Shen
中科院分区：
文献类型：
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作者：
Cheng Wang;Yi Shen
研究了不确定随机非线性时滞系统的非脆弱鲁棒随机镇定和鲁棒H∞控制问题。假设参数不确定性是时变的，范数有界，同时出现在状态矩阵和输入矩阵中。时滞是未知的，并且是时变的，有已知的界。非脆弱鲁棒随机镇定问题是设计一个无记忆的非脆弱状态反馈控制器，使闭环系统对所有允许的参数不确定性都是鲁棒随机稳定的。鲁棒H∞控制问题的目的除了鲁棒随机稳定性要求外，还在于将扰动输入对被控输出的影响减小到规定的水平。利用Lyapunov泛函方法和自由加权矩阵，用线性矩阵不等式（LMI）建立了这些问题可解性的时滞相关充分条件。数值算例表明了所提理论结果的有效性。
This paper deals with the problems of non-fragile robust stochastic stabilization and robust H∞control for uncertain stochastic nonlinear time-delay systems. The parameter uncertainties are assumed to be time-varying norm-bounded appearing in both state and input matrices. The time-delay is unknown and time-varying with known bounds. The non-fragile robust stochastic stabilization problem is to design a memoryless non-fragile state feedback controller such that the closed-loop system is robustly stochastically stable for all admissible parameter uncertainties. The purpose of robust H∞control problem, in addition to robust stochastical stability requirement, is to reduce the effect of the disturbance input on the controlled output to a prescribed level. Using the Lyapunov functional method and free-weighting matrices, delay-dependent sufficient conditions for the solvability of these problems are established in terms of linear matrix inequality (LMI). Numerical example is provided to show the effectiveness of the proposed theoretical results.