区间时变时滞线性系统的指数稳定性

Exponential Stability for Linear Systems with Interval Time-Varying Delays

基于Lyapunov泛函方法,研究时滞是时变的且属于一个区间的线性时滞系统的指数稳定性.以线性矩阵不等式的形式给出了一个新的指数稳定性判别准则.在估计Lyapunov泛函的导数时,利用凸组合和倒数凸组合方法得到了较小的上界,从而使得到的指数稳定性条件具有较小的保守性.另外,所得状态变量的指数上界只依赖于初始函数本身而不涉及其导数.最后,用数值算例验证了所得方法的有效性.

Based on the Lyapunov functional, exponential stability for linear systems with time- varying delay was studied. The time delay is a differentiable function belonging to a given interval. A new criterion for exponential stability was proposed in the form of linear matrix inequalities. When the derivative of the Lyapunov functional was estimated, a tighter upper bound was obtained using convex combination and reciprocally convex combination approaches that led to less conservatism of the condition for exponential stability. In addition, the obtained exponential upper bound of the state depended only on the initial function itself. An example was then presented to show the effectiveness of the proposed method.