Papers and Books used and related to the course material

[1]  Bogolyubov N.N. and Yu.A. Mitropolskii. Asymptotic methods in the theory of nonlinear oscillations. Gordon and Breach, N.Y., 1961.

[2]  Lyapunov A.M. The general problem of the stability of motion. Mathematical Society of Kharkov, 1892, (International Journal of Control, 55(3): 531-773).

[3]  Fradkov A.L. and A.Yu. Pogromsky. Introduction to control of oscillations and chaos. World Scientific Publishers, 1998.

[4]  Shiriaev A.S., J.W. Perram, C. Canudas-de-Wit. `Virtual constraints: a constructive tool for orbital stabilization of under-actuated nonlinear systems,’ IEEE Transactions on Automatic Control, vol. 50, no. 8, pp. 1164-1176, 2005

[5]  Shiriaev A.S., A. Robertsson, J.W. Perram, A. Sandberg. `Periodic Motion Planning for Virtually Constrained Euler-Lagrange Systems,’ Systems and Control Letters, vol. 55, no. 11, pp. 900-907, 2006.

[6]  La Hera P., L. Freidovich, U. Mettin, A.S. Shiriaev. `Swinging-up the Furuta pendulum via stabilization of preplanned trajectory: theory and experiments,’ IFAC Journal of Mechatronics, 19(8):1240-1250, 2009

[7]  Shiriaev A., L. Freidovich, I. Manchester. `Can we make a robot ballerina perform a pirouette? Orbital stabilization of periodic motions of underactuated mechanical systems,’ Annual Reviews in Control, vol. 32, no. 2, pp. 200-211, 2008.

[8]  Mettin U., P. La Hera, L. Freidovich, A. Shiriaev, J. Helbo. `Motion planning for humanoid robots based virtual constraints extracted from recorded human movements,’ Int. Journal of Intelligent Service Robotics, vol.1, no. 4, pp. 289 - 301, 2008.

[9]  Freidovich L., A. Robertsson, Shiriaev A., R. Johansson. `Stable Periodic Motions of the Pendubot via Virtual Holonomic Constraints: Theory and Experiments,’ Automatica, vol. 44, no. 3, pp. 785-791, 2008.

[10] Shiriaev A., L. Freidovich, A. Robertsson, R. Johansson, A. Sandberg. `Virtual Holonomic Constraint Based Design of Stable Oscillations of Furuta pendulum: Theory and Experiments,’ IEEE Transactions on Robotics, vol. 23, no. 4, pp.827-832, 2007.

[11] Shiriaev A.S. and L. Freidovich. `Transverse Linearization for Impulsive Mechanical Systems with One Passive Link,’ IEEE Transactions on Automatic Control, 54(12): 2882-2888,2009

[12] Shiriaev A.S., L. Freidovich and S. Gusev. `Transverse Linearization for Controlled Mechanical Systems with Several Passive Degrees of Freedom,’ IEEE Transactions on Automatic Control, Volume 55, April, 2010

[13] Mettin U., P. La Hera, L. Freidovich and A.S. Shiriaev. `Parallel Elastic Actuators as Control Tool for Preplanned Trajectories of Underactuated Mechanical Systems,’ International Journal of Robotics Research, 2010.

[14] Freidovich L., U. Mettin, A.S. Shiriaev, and M.W. Spong. `A Passive 2 DOF Walker: Hunting for Gaits Using Virtual Holonomic Constraints’, IEEE Transactions on Robotics, vol. 25, no. 5, pp. 1202–1208, 2009.

[15] Gusev S., S. Johansson, B. Kågström, A.S. Shiriaev, and A. Varga. `Numerical Evaluation of Solvers for the Periodic Riccati Differential Equation,’ BIT Numerical Mathematics, 29 p., June, 2010.

[16] Gusev S., A. Shiriaev and L. Freidovich. `LMI approach for solving periodic matrix Riccati equation,’ in Proc. of the 3rd IFAC workshop on Periodic Control Systems, 2007.

[17] Grizzle J.W., G. Abba, F. Plestan, `Asymptotically stable walking for biped robots: Analysis via systems with impulse effects', IEEE Transactions on Automatic Control, vol. 46, no. 1, pp. 51-64, 2001.

[18] Freidovich L., A. Shiriaev, I. Manchester, `Stability analysis and control design for an underactuated walking robot via computation of a transverse linearization,’ in Proc. of the 17th IFAC World Congress, 2008.

[19] Leonov G.A., `Generalization of the Andronov-Vitt Theorem', Regular and chaotic dynamics, vol. 11, no. 2, pp. 281–289, 2006.

[20] Westervelt E.R., J.W. Grizzle, C. Chevallereau, J.H. Choi, B. Morris, Feedback control of dynamic bipedal robot locomotion, Taylor & Francis / CRC Press, 2007.

[21] Urabe M., Nonlinear autonomous oscillations, Academic Press, N.Y., 1967.

[22] Banaszuk A., J. Hauser, `Feedback linearization of transverse dynamics for periodic orbits,´ Systems and Control Letters, vol. 26, pp. 95–105, 1995.

[23] Hill G.W. `On the part of the motion of the Lunar perigee which is a function of the mean motions of the Sun and Moon,' Acta Matematica, 1-36, 1886.