Distributed Average Consensus of Stochastic Singularly Perturbed Systems

The distributed consensus problems for singularly perturbed multiagent systems with noise are discussed in this study. By implementing Kalman-Bucy filtering when the communication topology satisfies connectivity conditions, the suggested protocol can produce a bounded average consensus. The benefit of such a protocol is that it helps to eliminate the ill-conditioning of solitary perturbation in systems and prevents the use of erroneous local information regarding the interconnection among agents in systems. The two main difficulties are designing control protocols using Kalman-Bucy filtering and decoupling using separation techniques. In particular, the convergence rate is examined along with
$\varepsilon$
-average consensus and
$\varepsilon$
-a.s. average consensus. By using numerical examples, theoretical analysis can be demonstrated.