Extensions of Invariance Principle with Applications in Multi-Agent Systems*

In this paper, we develop two extensions of invariance principle for nonlinear switched systems. We first present a union invariance principle for switched systems which shows that the switched solution approaches the combined zero loci of the output functions. Then, we extend the union weak-invariance principle to an intersection invariance principle, which greatly reduces the convergence region. Our new principles include as a special case the integral invariance principle. Finally, consensus problem of multi-agent systems with jointly connected topologies is solved using the principles.