Root
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Conference Proceedings
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3rd IFAC Workshop "PERIODIC CONTROL SYSTEMS" (PSYCO'07)
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Asymptotic stabilization of the desired uniform motion in
underactuated Hamiltonian systems by linear feedback
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In some cases the desired uniform motion may be described

by a pair of first integrals of the system with zero control input.

These two integrals and the integration of nonlinear function

of saturation are used to construct Lyapunov function

The control is designed from the condition of decreasing Lyapunov

function on the trajectories of the closed loop system. This

control may be chosen a priori bounded and linear in a small viciniti

of the desired motion. This method is applied to

stabilize rotating body beam, for damping the oscillations of

blades of an elastic propeller and for stabilization

of the uniform transition of the pendulum on a cart.

by a pair of first integrals of the system with zero control input.

These two integrals and the integration of nonlinear function

of saturation are used to construct Lyapunov function

The control is designed from the condition of decreasing Lyapunov

function on the trajectories of the closed loop system. This

control may be chosen a priori bounded and linear in a small viciniti

of the desired motion. This method is applied to

stabilize rotating body beam, for damping the oscillations of

blades of an elastic propeller and for stabilization

of the uniform transition of the pendulum on a cart.