Stabilization of Networked Control Systems with Sparse Observer-Controller Networks

In this paper we provide a set of stability conditions for linear time-invariant networked control systems with arbitrary topology, using a Lyapunov direct approach. We then use these stability conditions to provide a novel low-complexity algorithm for the design of a sparse observer-based control network. We employ distributed observers by employing the output of other nodes to improve the stability of each observer dynamics. To avoid unbounded growth of controller and observer gains, we impose bounds on their norms. The effects of relaxation of these bounds is discussed when trying to find the complete decentralization conditions.