On the exponential stability of nonlinear sampled-data systems with time-varying sampling periods

In this work we study the exponential stability of sampled-data systems consisting of the interconnection of a time-varying nonlinear continuous-time plant and a time-varying nonlinear discrete-time controller, assuming that the sampling periods are not necessarily constant. For this purpose we develop an indirect Lyapunov method of analysis, and show that under adequate hypotheses the exponential stability of the nonlinear system is equivalent to the exponential stability of its linearization.