Robustness analysis of digital feedback control systems with time-varying sampling periods

We study robustness properties of a class of digital feedback control systems with time-varying sampling periods consisting of an interconnection of a continuous-time nonlinear plant (described by systems of first-order ordinary differential equations), a nonlinear digital controller (described by systems of first-order ordinary difference equations), and appropriate interface elements between the plant and controller (A/D and D/A converters). For such systems, we establish results for exponential stability of an equilibrium (in the Lyapunov sense) in the presence of vanishing perturbations and for the boundedness of solutions (i.e., Lagrange stability) under the influence of non-vanishing perturbations. We apply these results to the study of quantization effects.