Dynamic feedback stabilization of a mechanical controlled system with distributed parameters (From the legacy of V. A. Yakubovich)

A control application involving a flexible-arm manipulator is considered. Its model is derived using Hamilton’s variational principle and, unlike other models, includes the effects of elastic strain induced by the driving hub. A control Lyapunov functional is constructed based on the energy identity, and stabilization is achieved using a dynamic linear compensator. This compensator is subject to the restrictions imposed by the Yakubovich–Kalman–Popov lemma. Asymptotic stability is established by applying the Barbashin–Krasovskii–LaSalle invariance principle to an associated system of coupled delay-differential and difference equations, whose solutions are in one-to-one correspondence with those of the basic closed-loop system.