Abstract
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.
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