Exponential stability of singularly perturbed switched systems with all modes being unstable - Yang, Wu (2021)
In this paper, we study the exponential stability problem for singularly perturbed switched systems(SPSSs), in which subsystems with two-time-scale property are all unstable, and both the destabilizing and stabilizing switching behaviors coexist. To estimate the state divergence during each two consecutive switching instants, the general property of a two-dimensional matrix involving singular perturbation parameter is explored. The switching sequence is properly reordered to provide an appropriate way to describe different switching behaviors. In addition, multiple composite Lyapunov functions(MCLFs) are employed to derive some stability criteria for the nonlinear SPSSs. Furthermore, by using switching-time-dependent MCLFs and dwell time method, some computable stability condition is given for the linear case. The obtained results show the relationship between the ratio of the stabilizing switching behavior and the singular perturbation parameter. Besides, the obtained results are free of ill-conditioning and stiffness problems.