基于Park积分不等式线性时滞广义系统稳定性分析

New Stability Analysis of Linear Singular Systems with Time Delays Based on Park's Integral Inequality

针对时滞系统稳定性问题,本文主要对一类时滞广义系统的稳定性进行研究。构造适当的Lyapunov-Krasovskii泛函,并对其中所构造的泛函进行适当的处理,并应用Park双重积分不等式方法以及Wirtinger型积分不等式方法进行处理,得到了新的判定时滞广义系统稳定性的充分条件。同时,通过对Matlab中的线性矩阵不等式工具箱的应用,来进行数值例子的求解以及验证,并通过本文得到的数据结果与以往相关文献中的数据进行比较分析。分析结果表明,本文的结果能够获得更大的时滞上界,验证了本文方法可以获得更小的保守性,进一步说明了本文结果的有效性和优越性。该结果对于深入研究时变时滞系统的稳定性及控制器设计都具有重要应用和意义。

This paper is concerned with the stability analysis for singular systems with time delays. F irs t ly , a suitable Lyapunov-Krasovskii functionals are constructed and the derivation of the constructed functional is cal-culated. Then by using Park’s double integral inequality and Wirtinger integral inequality method, a sufficient stability criterion is obtained. Mean while the conditions are in terms of linear matrix inequalities （LM Is） and a numerical example is given for illustration. Compared with some other methods, the computed results in this paper are better than the results in [14 -20] owing to obtaining upper bound of time-delay. These illustrate the results of this paper are effective and superior. The present method is of great significance for stability analysis of time-varying delay systems and design of controller.