线性奇异脉冲系统的稳定性分析

摘要

奇异脉冲系统是一类不连续的奇异系统，其状态在一系列离散时刻发生跳变。为充分刻画离散脉冲作用下奇异系统状态不连续的动态特征，提出基于时变 Lyapunov 函数的稳定性分析方法。通过运用此方法，并借助于凸组合技术，建立了一类奇异脉冲系统指数稳定性的充分条件。该稳定性条件以线性矩阵不等式形式给出，定量地揭示了脉冲区间及脉冲强度对系统稳定性影响。最后，用一个数值算例验证了所得结果的有效性。%Singular impulsive systems are a class of discontinuous singular systems where the state experiences jump at certain discrete instants.To fully characterize the discontinuous dy-namical feature of the system state under the impulse action,a method based on time-varying Lyapunov function is proposed for stability analysis.A sufficient condition for exponential sta-bility of linear singular impulsive systems is established by applying this method integrated with the technique of convex combination.The derived stability condition is expressed in terms of linear matrix inequalities,which quantitatively reveal the effects of impulsive intervals and impulse strength on system stability.Finally,a numerical example demonstrates the effective-ness of the obtained results.