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Semistability of Nonlinear Systems Having a Connected Set of Equilibria and Time-Delays

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1 Author(s)
Hui, Qing ; Dept. of Mech. Eng., Texas Tech Univ., Lubbock, TX, USA

In this technical note, we develop a semistability analysis framework for nonlinear systems with bounded time-varying delays with applications to stability analysis of multiagent dynamic networks with consensus protocols in the presence of unknown heterogeneous time-varying delays along the communication links. We show that for such a nonlinear system having nonisolated equilibria, if the system asymptotically converges to a constant time-delay system and this new system is semistable, then the original time-varying delay system is semistable. In proving our results, we extend the limiting differential equation approach to time-varying delay systems and also develop some new convergence results for functional differential equations.

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Automatic Control, IEEE Transactions on  (Volume:57 ,  Issue: 10 )