Output formation-containment of interacted heterogeneous linear systems by distributed hybrid active control

This paper investigates the output formation-containment problem of interacted heterogeneous linear systems, where each heterogeneous system, whether the leader or the follower, has different dimensions and dynamics. Different from existing literature, discrete-time communication manner is deployed to reduce the communication consumption. By the impulsive control method, a distributed hybrid active controller is designed using the discrete-time information of neighbors. It achieves the output formation-containment of heterogeneous systems if two related conditions are satisfied, namely, local linear matrix inequalities (LMIs) and a bounded constraint on the average interacted interval. Moreover, the controller parameter design is further simplified by replacing the LMI condition with a Hurwitz condition, which can be easily guaranteed by solving a Riccati equation. Finally, a numerical example is provided to demonstrate the effectiveness of the theoretical result.