A Weighted H∞ Consensus Achievement for LTI Multi-Agent Systems with Directed and Switching Topology Networks

Abstract

The consensus problem with a weighted H∞ bound for a homogeneous team of linear time-invariant (LTI) multi-agent systems with a switching topology and directed communication network graph is studied in this paper. A design methodology is proposed based on the solution of an algebraic Riccati equation without the need to solve linear matrix inequalities (LMIs). The design procedure is in two steps. First, agents are made marginally stable by using a local state feedback controller. In the second step, a relative state feedback controller is designed to achieve consensus. It is worth pointing out that these steps can be performed independently. The stability of the proposed controller is investigated based on Lyapunov stability analysis. The effectiveness of the proposed consensus algorithm is illustrated by performing numerical simulations.