Controllability of impulsive singularly perturbed systems and its application to a class of multiplex networks. (February 2019) - Yang, Wu
Abstract: This paper is concerned with the controllability problem of impulsive singularly perturbed systems (ISPSs). A new analytical approach is developed by integrating the merits of the fast–slow decomposition, Chang transformation and Gram-like matrix, and then some ε -independent necessary and sufficient controllable conditions are obtained. In addition, the upper bound of ε is given when deriving the sufficient controllable conditions. Moreover, a new type of heterogeneous multiplex multi-time-scale networks is introduced and can be further modeled by ISPSs. Based on matrix theory and graph theory, some intuitive and easy-to-test criteria are deduced for the controllability of the proposed networks. It is shown that the network topology, the nodal dynamics, the leader selection, and the inner-coupling interconnection are important controllable factors. Several numerical examples are presented to show the effectiveness of the proposed results. Highlights: An effective analytical method is developed to solve the controllability problem of impulsive singularly perturbed systems. Both the sufficient and necessary controllable conditions are derived. The upper bound of singular perturbation parameter is deduced explicitly to ensure the controllability of the system. A new class of impulsive multilayer multi-time-scale networks is introduced and some controllability factors are revealed.