Consensus Problem of Discrete-Time Linear Multi-agent Systems with Non-convex Control Input and State Constraints

In this article, a consensus problem of discrete-time multi-agent systems with control input and state constraints, switching topologies and linear dynamics is studied. A consensus algorithm in view of the state of agent itself and its local information is proposed. The consensus analysis of system is based on selecting parameter matrices properly, transforming model, exploring the convexity of stochastic matrices, and eventually proving the states of agents in system with direct spanning trees will tend to be consistent. Finally, we display a numerical example to confirm the truth of our theory.