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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.
For a linear time-delay system with multi-state delay, it is first described as a feedback interconnected system, which uses the bounded operator associated with the delay to describe the uncertainty of the feedback system and reduces it by the artificial division of the time-delay Small Conservatives. Based on the Lyapunov theory, the stability of the system is analyzed. A less conservative asymptotic stability condition is obtained in the form of LMI. The conclusion can more fully reflect the state history information of the system. The smaller the classification, the less conservative , The example shows that only the rough division can greatly improve the conservative performance, in order to take into account the computational burden, r take a small value can be and LMI in the decision-making less, simple form.