Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-09T14:29:21.611Z Has data issue: false hasContentIssue false

Input-to-state stability with respect to measurement disturbances for one-dimensional systems

Published online by Cambridge University Press:  15 August 2002

Nicolas Chung Siong Fah*
Affiliation:
École Normale Supérieure, 45 rue d'Ulm, 75005 Paris, France; [email protected].
Get access

Abstract

We consider one-dimensional affine control systems. We show that if such a system is stabilizable by means of a continuous, time-invariant feedback, then it can be made input-to-state stable with respect to measurement disturbances, using a continuous, periodic time-varying feedback. We provide counter-examples showing that the result does not generally hold if we want the feedback to be time-invariant or if the control system is not supposed affine.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 1999

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Sontag, E.D., Smooth stabilization implies coprime factorization. IEEE Trans. Automat. Cont. 34 (1989) 435-443. CrossRef
Freeman, R., Global internal stabilizability does not imply global external stabilizability for small sensor disturbances. IEEE Trans. Automat. Contr. 40 (1996) 2119-2122. CrossRef
R. Freeman and P. Kokotovic, Robust nonlinear control design - state-space and Lyapunov techniques, Birkhäuser, Boston Basel Berlin (1996).
E.D. Sontag, Mathematical control theory: Deterministic Finite Dimensional Systems, Text in Applied Mathematics 6, Springer-Verlag, New York Berlin Heidelberg (1990).
C. Samson, Velocity and torque feedback control of a nonholomic cart, in Robot Control, Proc. of the International Workshop on Nonlinear and Adaptive Control: Issues in Robotics, C. Canudas de Wit Ed., Grenoble, France, November 21-23, 1990, Springer-Verlag, Berlin Heidelberg New York, Lecture Notes in Control and Information Sciences 162 (1991) 125-151.
Coron, J.M., Global asymptotic Stabilization for controllable systems without drift. Math. Control Signals Systems 5 (1992) 295-312. CrossRef
Coron, J.M., Stabilization in finite time of locally controllable systems by means of continuous time-varying feedback laws. SIAM J. Contr. Opt. 33 (1995) 804-833. CrossRef
Coron, J.M., On the stabilization of controllable and observable systems by an output feedback law. Math. Control Signals Systems 7 (1994) 187-216. CrossRef
R. Freeman, Time-varying feedback for the global stabilization of nonlinear systems with measurement disturbances, in Proc. European Control Conference, Brussels (1997).
N.N. Krasovskii, Stability of motion, Standford University Press, Standford (1963).
J.M. Coron, L. Praly and A. Teel, Feedback stabilization of nonlinear systems: sufficient conditions and Lyapynov and Input-output techniques, in Trends in Control, A. Isidori Ed., Springer-Verlag (1995) 293-348.
Sontag, E.D. and Wang, Y., New characterizations of the input to state stability property. IEEE Trans. Automat. Contr. 41 (1996) 1283-1294. CrossRef
Y. Lin, Input-to-state stability for noncompact sets Proc. 13th IFAC World Congress, Vol. E, San Francisco (1996) 73-78.