H∞ delayed tracking protocol design of nonlinear singular multi-agent systems under Markovian switching topology

© 2020 Elsevier Inc. The consensus tracking of singular multi-agent systems (MASs) with Lipschitz-type nonlinearities and exogenous disturbances is researched in this paper. Governed by a Markov chain, the network interaction randomly switches in a directed graph set, where the directed spanning tree is not contained in each graph while exists in the union rooting at the leader node. By utilizing a collection of in-neighbors’ information that involves communication delay, the intention is to design a protocol such that the resultant consensus error system is stochastic admissible with an H∞ disturbance attenuation level. Based on algebraic graph theory, stochastic admissibility analysis and linear matrix inequality (LMI) technique, tracking consistency is first regulated in the concerned MAS by considering the case of completely known transition probabilities. Then, thanks to a group of free-connection weighting matrices, the obtained result is extended to the case that transition probabilities are partially known. Finally, the theoretical analysis is confirmed by some numerical examples