Stability analysis of sliding-mode feedback control

• Autorzy: Clarke F. H. , Vinter R. B.
• Języki publikacji: EN

Abstrakty

EN

This paper provides new analytic tools leading to the first rigorous stability and robustness analysis of sliding-mode feedback controllers. Unrestrictive conditions are given, under which these controllers are stabilizing in the presence of large disturbances, conditions invoke the existence of two Lyapunov-type functions, the first associated with passage to the sliding set in finite time, and the second with convergence to the desired state. In this approach, account is taken, from the outset, of implementational constraints. We provide a framework for establishing stability and robustness of the closed-loop system, for a variety of implementation schemes. We illustrate our results by means of two examples of the type frequently encountered in the sliding-mode literature.

Słowa kluczowe

EN

sliding-mode control; discontinuous control; Lyapunov functions; stabilization; robustness

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2009
• Tom: Vol. 38, no 4A
• Strony: 1169--1192
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Clarke F. H.

autor

Vinter R. B.

• Institut universitaire de France et Universite de Lyon, Institut Camille Jordan, 69622 Villeurbanne, France

Bibliografia

• CLARKE, F., LEDYAEV, Y.S., RIFFORD, L. and STERN, R. (2000) Feedback stabilization and Lyapunov functions. SIAM J. Control Optim. 39, 25-48.
• CLARKE, F., LEDYAEV, Y.S., SONTAG, E.D. and SUBBOTIN, A.I. (1997) Asymptotic controllability implies feedback stabilization. I.E.E.E. Trans. Aut. Control 42, 1394-1407.
• EDWARDS C. and SPURGEON S.K. (1998) Sliding Mode Control. Taylor and Francis, London.
• FILIPPOV, A.F. (1988) Differential Equations with Discontinuous Righthand Sides. Kluwer Academic Publishers, Dordrecht.
• LEDYAEV, Y.S. and SONTAG, E.D. (1999) A Lyapunov characterization of robust stabilization. Nonlinear Analysis 37, 813-840.
• SLOTINE, J.J.E. and LI, W. (1991) Applied Nonlinear Control. Prentice Hall, Englewood Cliffs NJ.
• SONTAG, E.D. (1999) Stability and stabilization: discontinuities and the effect of disturbances. In: F. Clarke and R. Stern, eds., Nonlinear Analysis, Differential Equations and Control. NATO ASI, Montreal 1998. Kluwer Acad. Publ., Dordrecht, 551-598.
• UTKIN, V.I. (1992) Sliding Modes in Control Optimization. Springer Verlag, Berlin.
• WILLEMS, J.L. (1970) Stability Theory of Dynamical Systems. Thomas Nelson and Sons, London.
• YOUNG, K.D., UTKIN, V.I. and ÖZGÜNER, Ü. (1999) A control engineer’s guide to sliding mode control. IEEE Trans. Control Sys. Tech. 7, 328-342.