On finite-time stability for nonlinear impulsive switched systems - Wang, Yijing; Shi, Xiaomeng; Zuo, Zhiqiang; Chen, Michael Z.Q.; Shao, Yitian (Nonlinear analysis: real world applications, 2013)
This paper is concerned with the finite-time stability problem for switched systems subject to both nonlinear perturbation and impulse effects. The average dwell time approach, combined with the algebraic matrix theory, is utilized to derive a criterion guaranteeing that the state trajectory does not exceed a certain threshold over a pre-specified finite-time interval. The requirement that at least one subsystem should be stable to ensure asymptotic stability is no longer necessary. Moreover, the finite-time stability degree could be positive, which is a relaxed condition for asymptotic stability. A numerical example is presented to illustrate the effectiveness of the proposed method.