Time-varying formation control via output feedback for multi-agent systems over switching networks with hidden Markov dynamics

This paper addresses time-varying formation control for a class of multi-agent systems. In particular, distributed static output control laws are designed for homogeneous discrete-time linear multi-agent systems whose network topologies switch according to an unknown Markov chain θ . We assume the existence of an estimator θ ̂ for the mode of operation of the network topology θ , so that the joint process ( θ , θ ̂ ) can be viewed as a hidden Markov chain. The proposed local output controllers switch based on the information from the estimator θ ̂ to enforce the desired, global time-varying formation. The control design also aims to optimize performance indices based on the H 2 , H ∞ criteria, as well as a mixed H 2 / H ∞ criterion. All problems are formulated as linear matrix inequalities, enabling the application of standard numerical tools. The results are illustrated by means of numerical examples.