A stability property of nonlinear sampled-data systems with slowly varying inputs

A stability analysis is presented that deals with the response of a nonlinear sampled-data system to a slowly varying exogenous input signal. The main result, similar to existing results for purely continuous-time and discrete-time systems, establishes that if the system possesses a manifold of exponentially stable constant operating points (equilibria) corresponding to constant values of the input signal, then an initial state close to this manifold and a slowly varying input signal yield a trajectory that remains close to the manifold. The analysis involves casting the sampled-data system as a continuous-time system with discrete jumps at the sampling instants.