Consensus of Discrete-time Positive Multi-agent Systems with Observer-type Protocols

This paper studies the consensus problem for discrete-time positive multi-agent systems with an observer-type dynamic output-feedback protocol. Each agent’s dynamics is defined by linear positive systems and the communication topology is modelled by an undirected graph. When studying the consensus problem in the framework of semi-definite programming, it is demonstrated that distributed state-feedback controller and observer should be designed to ensure the positivity of multi-agent systems. By using positive systems’ characteristics and graph theory, necessary and sufficient conditions for the design of both state-feedback controller and observer for consensus are derived by virtue of the solutions of matrix inequalities. Numerical simulations are provided to demonstrate the validity and applicability of the above theoretical results and algorithm.