Observer-Based Consensus for Multi-Agent Systems With Semi-Markovian Jumping Via Adaptive Event-Triggered SMC

This paper investigates the observer-based event-triggered adaptive sliding mode control (SMC) problem of the semi-Markovian jumping multi-agent systems (S-MJMASs) with completely unknown and uncertain bounded transfer probabilities (TPs). As impacted by the limited bandwidth of the communication network between individual agents and the unmeasurable state information of the systems, an innovative observer based distributed event-triggered adaptive mechanism (ETAM) is proposed, in which the global information of the network is not used and the triggering threshold is dynamically regulated by the adaptive law to reduce excessive network communication. Additionally, since delays exist between the event trigger and the zero-order holder (ZOH) during data transmission in network communication systems, as well as the semi-Markovian jumping parameters, the uncertainty of systems is increased. In this paper, a novel integral sliding surface is constructed and its reachability and continuity in stochastic senses are guaranteed to withstand interferences. With the help of a stochastic semi-Markovian Lyapunov functional and numerous linear matrix inequalities (LMIs) approaches, certain adequate conditions are achieved to ensure that all agents in S-MJMASs can track the leader. Finally, certain numerical simulations are used to demonstrate the efficiency of the suggested theoretical conclusions.