Lyapunov Functions for Persistently-Excited Cascaded Time-Varying Systems: Application to Consensus

We present some results on stability of linear time-varying systems with particular structures. Such systems appear in diverse problems, which include the analysis of adaptive systems, persistently-excited observers and consensus of systems interconnected through time-varying links. The originality of our statements rely in the fact that we provide smooth strict Lyapunov functions hence, our proofs are constructive and direct. Moreover, we establish uniform global exponential stability with explicit stability and decay estimates. For illustration, we address a brief but representative case-study of consensus of Lagrangian systems interconnected through unreliable links.