Exponential stabilizability of nonlinear control systems in Banach spaces

Abstract

This paper deals with the problem of stabilizability of perturbed linear time-varying control systems in Banach spaces. Assuming appropriate conditions on the perturbation term, it is shown that if every frozen-time control system is stabilizable then the corresponding non-autonomous control system is exponential stabilizable, provided the rate of variation of the system coefficient operators is sufficiently small. This approach is based on the extension of the freezing technique to infinite-dimensional Banach spaces. Sufficient conditions for the exponential feedback stabilizability of a class of time-varying nonlinear systems are established. The obtained results extend existing results in the literature to infinite-dimensional control systems.

Keywords:

• Time-varying systems
• feedback stabilization
• freezing method
• Banach space
• linear operator

AMS Subject Classifications:

• 34K20
• 47D06

Acknowledgements

The author is grateful to anonymous referees for their careful review and encouraging comments.

Notes

No potential conflict of interest was reported by the author.

Additional information

Funding

This research was supported by Fondo Nacional de Ciencia y Tecnologia(Fondecyt) Chile [grant number 1130112].