Leader-follower tracking control with guaranteed consensus performance for interconnected systems with linear dynamic uncertain coupling

This paper considers the leader-follower tracking control problem for linear interconnected systems with undirected topology and linear dynamic coupling. Interactions between the systems are treated as linear dynamic uncertainty and are described in terms of integral quadratic constraints (IQCs). A consensus-type tracking control protocol is proposed for each system based on its state relative its neighbors. In addition a selected set of subsystems uses for control their relative states with respect to the leader. Two methods are proposed for the design of this control protocol. One method uses a coordinate transformation to recast the protocol design problem as a decentralized robust control problem for an auxiliary interconnected large scale system. Another method is direct, it does not employ coordinate transformation; it also allows for more general linear uncertain interactions. Using these methods, sufficient conditions are obtained which guarantee that the system tracks the leader. These conditions guarantee a suboptimal bound on the system consensus and tracking performance. The proposed methods are compared using a simulation example, and their effectiveness is discussed. Also, algorithms are proposed for computing suboptimal controllers.