Weighted bipartite containment motion of impulsive cooperative-competitive harmonic oscillators

The present paper investigates weighted bipartite containment control of coupled harmonic oscillators with instantaneous cooperative-competitive interactions. A control scheme is proposed by introducing instantaneous cooperative-competitive interactions, where every harmonic oscillator can obtain different levels of positive and negative information from its neighbors only at some impulsive time moments. Based on this, some conditions on the networked structure, the coupling strengthen, and the impulsive time interval are developed to guarantee that the followers can converge to the weighted intervals, which are determined by every leader's weighted state and its symmetric weighted state. The results are supported with an illustrative example.