Full Text

1

CITATION

1 Total citation

0 Recent citations

0.22 Field Citation Ratio

n/a Relative Citation Ratio

publications

0

supporting

0

mentioning

0

contrasting

0

Smart Citations

0

0

0

0

Citing PublicationsSupportingMentioningContrasting

View Citations

See how this article has been cited at scite.ai

scite shows how a scientific paper has been cited by providing the context of the citation, a classification describing whether it supports, mentions, or contrasts the cited claim, and a label indicating in which section the citation was made.

• M. Athans and P. L. Falb. Optimal control: an introduction to the theory and its applications. McGraw-Hill, 1966.
• A. Bressan and B. Piccoli. A generic classification of time-optimal planar stabilizing feedbacks. SIAM Journal on Control and Optimization, 36(1): 12-32, 1998.
• R.T. Buppo, D.S. Bernstein, V.S. Chellaboina, and W.M. Haddad. Finite settling time control of the double integrator using a virtual trap-door absorber. IEEE Transactions on Automatic Control, 45(4):776-780, 2000.
• F.H. Clarke. Optimization and Nonsmooth Analysis. Society for Industrial an Applied Mathematics, 1990.[
• D.S. Bernstein F. Tyan. Global stabilization of systems containing a double integrator using a saturated linear controller. International Journal of Robust and Nonlinear Control, 9(15); 1143-56, 1999.
• Haijun Fang and Zongli Lin. Global practical stabilization of planar linear systems in the presence of actuator saturation and input additive disturbance. IEEE Transactions on Automatic Control, 51(7); 1177-1184, 2006.
• J.Y. Favez, Ph. Mullhaupt, B. Srinivasan, and D. Bonvin. Attraction region of planar linear systems with one unstable pole and saturated feedback. Journal of Dynamical and Control Systems, 12(3):331-355, 2006.
• A.T. Fuller. In-the-large stability of relay and saturating control systems with linear controllers. Int. J. Contr., 10:457-480, 1969.
• Z. Galias. Finite switching frequency effects in the sliding mode control of the double integrator system. Proc. of the IEEE International Symposium on Circuits and Systems (ISCAS), pages 2145-2148, 2006.
• C.E. George and R.T. O'Brien Jr. Vehicle lateral control using a double integrator control strategy. In Proceedings of the Thirty-Sixth Southeastern Symposium on System Theory, pages 398-400, 2004.
• W. Hahn. Stability of Motion. Springer-Verlag, 1967.
• W.X. Jing and C.R. McInnes. On the øp-stabilization of the double integrator subject to input saturation. ESAIM Control, Optimisation and Calculus of Variations, 6:291-331, 2001.
• W.X. Jing and C.R. McInnes. Memorised quasi-time-fuel-optimal feedback control of perturbed double integrator. Automatica, 38(8):1389-96, 2002.
• C.Y. Kao, On the L2-gum of a double integrator with feedback loop saturation nonlinearity. IEEE Transactions on Automatic Control, 46(3):501-504, 2001.
• H.K. Khalil. Nonlinear Systems. Prentice Hall, USA, 3rd edition, 2002.
• J. Kurzweil. On the inversion of Ljapunov's second theorem on stability of motion. American Mathematical Society Translations, ser. 2, 24:19-77, 1956.
• W. Lan, B.M. Chen, and Y. He. On improvement of transient performance in tracking control for a class of nonlinear systems with input saturation. Systems & Control Letters, 55(2):132-138, 2006.
• N. Marchand and H. Ahmad. Global stabilization of multiple integrators with bounded controls. Automatica, 41(12):2147-2152, 2005.
• F. Morabito, A.R. Teel, and L. Zacearian. Nonlinear anti-windup applied to Euler-Lagrange systems. IEEE Trans. Rob. Aut. (A), 20(3):526-537, 2004.
• V.G. Rao and D.S. Bernstein. Naive control of the double integrator. Control Systems Magazine, 21(5):86-97, 2001.
• W.E. Schmitendorf and B.R. Barmish. Null controllability of linear systems with constrained controls. SIAM J. Contr. Opt., 18(4):327-345, July 1980.
• G. Shi and A. Saberi. On the input-to-state stability (ISS) of a double integrator with saturated linear control laws. In Proc. of the American Control Conference, pages 59-61, 2002.
• JJ. Slotine and S.S. Sastry. Tracking control of non-linear systems using sliding surfaces, with application to robot manipulators. Int. Journal of Control, 38(2):465-492, 1983.
• E.D. Sontag. An algebraic approach to bounded controllability of linear systems. Int. Journal of Control, 39(1):181-188, 1984.
• R. Suarez, J. Alvarez-Ramirez, and B. Source. First harmonic analysis of planar linear systems with single saturated feedback. International Journal of Bifurcation and Chaos, 6(12):2605-10, 1996.
• H. J. Sussmann. The structure of time-optimal trajectories for single-input systems in the plane: The general real analytic case. SIAM Journal on Control and Optimization, 25(4):868-904, 1987.
• H.J. Sussmann and Y. Yang. On the stabilization of multiple integrators by means of bounded feedback controls. In 30th CDC, pages 70-72, Brighton, England, Dec 1991.
• A.R. Teel A nonlinear small gain theorem for the analysis of control systems with saturation. IEEE Transactions on Automatic Control, 41(9):1256-1270, Sep. 1996
• A.R. Teel and L. Praly. A smooth Lyapunov function from a class-KL estimate involving two positive semidefinite functions. ESAIM: Control, Optim. Calc. of Variations, 5:313-367, 2000.
• A.R. Teel and L. Zaccarian. On "uniformity" in definitions of global asymptotic stability for time-varying nonlinear systems. Automatica, 42(12):2219-2222, 2006.