Impulsive Containment Control for Linear Multi-Agent Systems with Self-Feedback and Aperiodic Sampling

In this paper we discuss the impulsive containment control problem of continuous-time linear multi-agent systems. Firstly, an impulsive control protocol with self-feedback and aperiodic sampling is proposed, in which the coupling matrix do not have to be Laplacian. Utilizing the proposed protocol, the impulsive containment control problem for continuous-time linear multi-agent systems is equivalently transformed into the stabilization problem of some independent linear discrete-time switched systems. Then a mode-dependent switching-type Lyapunov function is constructed, some sufficient conditions are showed by using some linear matrix inequalities to achieve the containment control purpose. In addition, based on a linear matrix inequality, the controller gain matrix can be designed to solve the containment control problem. In obtained results, the self-feedback gain, the size and the switching frequency of the sampling intervals can play all important roles. Finally, two simulation examples are employed to validate the effectiveness of the theoretical results.