Minimum-time and minimum-triggering impulsive stabilization for multi-agent systems over finite fields

Abstract

This paper investigates the problem of stabilization for multi-agent systems over finite fields via two types of impulsive control, that is, time-triggered impulsive control (TTIC) and state-triggered impulsive control (STIC). Inspired by the fact that finite-field networks (FFNs) cannot achieve stability at a nonzero state over the finite fields F p , p > 2 , two kinds impulse-controlled FFNs (ICFFNs) are introduced subject to time-triggering sequence and state-triggering set, respectively. In order to save time and control cost, the minimum-time control and minimum-triggering control of FFNs are both investigated. The time-optimal and triggering-optimal TTIC and STIC are successively designed. It reveals that designing such optimal TTIC for stabilizing ICFFNs can be transformed into finding the shortest path in the pretreated transition graph, and designing such optimal STIC for the global stabilization of ICFFNs is converted into finding the minimum spanning in-tree. Two examples are given to illustrate the control design procedures. Finally, we discuss the applications of the proposed control design methods on the synchronization problem and the switched FFNs including deterministic switched FFNs, probabilistic FFNs and Markovian jumping FFNs.