New relationships between Lyapunov functions and the passivity theorem

In this paper we study new relationships between a class of Lyapunov functions and the passivity theorem. It is proved that under some (sufficient) conditions a Lyapunov-stable system can be analysed as the feedback connection of two (strictly) passive subsystems. It is also shown that very recent adaptive schemes for linear plants of any relative degree can in a certain sense be unified through a passivity point of view.

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