时滞相关的多状态时滞系统稳定性分析

Delay-Dependent Stability Analysis for Multiple-State Delays Systems

对于存在多状态时滞的线性时滞系统,首先将其重新描述为反馈互联系统,利用与时滞相关的有界算子来描述反馈系统的不确定性,并通过人为划分时滞量来减小保守性,基于Lyapunov理论分析稳定性,得到以LMI形式给出的一种保守性小的渐近稳定性条件,结论中能够更加全面的反映系统的状态历史信息,划分越细则保守性越小,实例表明只需粗略划分就能大大提高保守性能,为了兼顾计算负担,r取较小数值即可.并且LMI中的决策变量少,形式简洁.

This paper investigates the stability of multiple-state delays linear time delay systems. Rewriting the delay system as an interconnected feedback form at first, and then the uncertainty can be described as certain delay dependent bounded operators. The conservatism can be reduced through the delay fractioning. The criteria of stability is derived based on the Lyapunov theory and is formulated as feasibility problems of Linear Matrix Inequalities, and the criteria includes more information about the states. The conservatism is reduced as the delay fractioning grows. Numerical examples indicate that the performance of conservatism will be improved notably even by coarse fractioning. In order to make a tradeoff between conservatism and computational complexity the less fractioning can be used practically, and with fewer decision variables in LMIs.