时变时滞切换系统的指数稳定性及L2增益分析

发布时间：2018-04-19 02:38

本文选题：切换系统 + 指数稳定性　；参考：《沈阳师范大学学报(自然科学版)》2016年03期

【摘要】：研究时变时滞切换系统的指数稳定性及相应的L2增益分析问题。构建了一类限定时滞上界和下界的特殊分段Lyapunov-Krasovskii函数,通过时滞分解方法及Jensen积分不等式与倒数凸组合相结合的技术处理了分段Lyapunov-Krasovskii函数中的积分项。更进一步,在估计泛函微分的上界过程中,一方面,未引入加权矩阵,从而涉及较少的决策变量,降低了计算复杂性;另一方面,未忽略任何有效信息,因此获得了具有更小保守性的稳定性结论。此外,利用平均驻留时间的方法给出了时变时滞切换系统的指数稳定性及L2增益的充分条件,同时也给出了切换律的设计方案。最后,将时变时滞切换系统的稳定性及L2增益分析问题归结为线性矩阵不等式的求解问题,这样便于利用Matlab工具箱求解并验证结论有效性。
[Abstract]:The exponential stability and L2 gain analysis of switched systems with time-varying delays are studied.A class of special piecewise Lyapunov-Krasovskii functions with limited upper and lower bounds of delay is constructed. The integral terms in piecewise Lyapunov-Krasovskii functions are treated by the method of time-delay decomposition and the combination of Jensen integral inequality and reciprocal convexity.Furthermore, in the process of estimating the upper bound of functional differential, on the one hand, the weighting matrix is not introduced, which involves less decision variables, thus reducing the computational complexity; on the other hand, no valid information is ignored.Therefore, a stability conclusion with less conservatism is obtained.In addition, the sufficient conditions for exponential stability and L2 gain of switched systems with time-varying delays are given by using the method of mean dwell time, and the design scheme of switching law is also given.Finally, the problem of stability and L2 gain analysis of switched systems with time-varying delays is reduced to the solution of linear matrix inequalities (LMIs), which is easy to solve by using the Matlab toolbox and verify the validity of the conclusions.
【作者单位】：沈阳师范大学数学与系统科学学院;
【基金】：国家自然科学基金资助项目(11201313)
【分类号】：TP13

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