一类区间时变时滞系统的稳定性分析

摘要

针对一类区间时变时滞系统的稳定性问题,进行了全局渐近稳定性分析.通过引入时滞分段方法和构建恰当的Lyapunov-Krasovskii泛函,得到了新的区间时滞相关稳定性判定准则.该准则以线性矩阵不等式形式给出,便于利用LMI工具箱对系统的稳定性进行判定.新准则具有较少的保守性,并且在一定范围内保守性随着时滞分段增多而减少,即时滞分段越多,保守性越少.数值仿真算结果例表明了新准则所具有的有效性和较少的保守性.%Aimed at the problem of the stability of systems with time-varying delay in a range, the global asymptotic stability a-nalysis of delay-range-dependent systems with time-varying delays is investigated. A new criterion of the delay-range-dependent stability is derived by introducing an appropriate type of Lyapunov-Krasovskii functional with the idea of delay fractioning and is formulated in terms of a linear matrix inequality (LMI), which can be readily solved via LMI Toolbox. This new criterion based on a delay fractioning approach proves to be much less conservative and the conservatism could be notably reduced by thinning the delay fractioning within a certain range. Finally, a numerical example is given to demonstrate the effectiveness and the less conservative of the proposed criterion.