Global Exponential Stability Preservation under Sampling and Approximated Delay-Dependent Feedbacks for Nonlinear Systems with Time-Varying Delays

This manuscript shows the global exponential stability preservation for the class of fully nonlinear retarded globally Lipschitz systems with time-varying delays under suitably fast sampling, while considering at the same time the problem of the non-availability in the buffer device of the system variables at some past (delayed) times. To this aim, a spline interpolation scheme is exploited to derive the digital control law, which has the benefit of ease of implementation. Main theoretical results are achieved by means of Halanay's inequality. The knowledge of a Lyapunov-Krasovskii functional is not required as long as the system at hand is globally exponentially stabilizable by a globally Lipschitz feedback in continuous time. Its knowledge is needed to quantify a maximum sampling period.