On stabilisability of nonlinear systems on time scales

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.

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