一种改进的区间时变时滞系统稳定性准则

An Improve Stability Criterion for Systems with Interval Time-varying Delay

研究区间时变时滞系统的稳定性问题。首先,通过引入一个区间调节参数,将系统时滞区间分解为两部分之和。其次,在两个子区间的基础上构造一个包含更多时滞信息和三重积分项的新Lyapunov-Krasovskii (L-K)泛函。在处理来自L-K泛函求导过程中产生的积分交叉项时,将时滞分属于各子区间的情况作为一个整体来研究。然后,基于Lyapunov稳定性理论,以线性矩阵不等式的形式给出一个新的稳定性准则。最后,通过两个数例证明所得稳定性准则的有效性。

The problem of stability for systems with interval time-varying delay is concerned in this paper. Firstly, the delay interval of systems is decomposed into two sub-intervals by introducing an interval adjusting parameter. Secondly, on the basis of each sub-interval, a new Lyapunov-Krasovskii(L-K) functional, which includes more information of delay and some new triple-integral terms, is constructed. In the process of dealing with the integral cross terms from the derivation of L-K functional, the case of time-varying delay falling, respectively, into each sub-interval are lumped into an unit to study. Thirdly, based on Lyapunov stability theory, a new delay-dependent stability criterion is proposed in the form of linear matrix inequalities. Finally, the effectiveness of the proposed stability criterion is demonstrated via two examples.