Stabilization of Nonlinear Mechanical Systems with Partial Measurement of the Generalized Coordinates
Systems with deficiency of control forces and measurement only parts of the generalized coordinates are considered. The method of stabilization of equilibrium position, based on introduction of auxiliary coordinates and application of energy approach with use of a total energy of expanded system as Lyapunov's function is offered. For essentially nonlinear systems with generally homogeneous potential energy three cases in which the equilibrium position can be stabilized to global asymptotic stability are revealed.
1. Rumjancev V.V., Oziraner, A.S. Stability and Stabilization of Motion with Respect to Part of Variables. Moscow, Nauka, 1987, 256 p. (in Russian).
2. Vorotnikov V.I., Rumjancev, V.V. Stability and Control with Respect to part Coordinates of Phase Vector of Dynamical Systems: Theory, Methods and Applications. Moscow, Scientific World, 2001. 320 p. (in Russian).
3. Lee Y.S., Vakakis A.F., Bergman L.A., McFarland D.M., Kerschen G., Nucera F., Tsakirtzis S., Panagopoulos P.N. Passive Non-Linear Targeted Energy Transfer and its Applications to Vibration Absorption: a Review. Proceedings ofthe Institution ofMechanical Engineers. Part K. Journal ofMulti-body Dynamics, 2008, vol. 222, no. 2, pp. 77-134.
4. Fantoni I., Lozano R. Non-Linear Control for Underactuated Mechanical Systems. Springer, 2002. 295 p.
5. Barbashin E.A., Krasovsky N.N. On the Stability of Motion in the Large. Doklady Akad. Nauk SSSR, 1952, vol. 86, no. 3, pp. 453-456. (in Russian).
6. Krasovsky N.N. Some Problems of the Theory of Stability of Motion.Moscow, GIFML, 1959. 211 p. (in Russian).
7. Zubov V.I. Mathematical Methods for the Study of Automatic Control Systems. New York etc., Pergamon Press Yerusalem, Academic Press, 1962. 327 p.