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.