On stabilisability of nonlinear systems on time scales

Abstract

In this article, stabilisability of nonlinear finite-dimensional control systems on arbitrary time scales is studied. The classical results on stabilisation of nonlinear continuous-time and discrete-time systems are extended to systems on arbitrary time scales with bounded graininess function. It is shown that uniform exponential stability of the linear approximation of a nonlinear system implies uniform exponential stability of the nonlinear system. Then this result is used to show a similar implication for uniform exponential stabilisability.

Keywords:

• control system
• stabilisability
• uniform exponential stability
• time scale

Acknowledgements

This work was supported by the Bialystok University of Technology grant S/WI/2/2011.