Robustness Analysis of Piecewise Dynamical Cycles

A general perturbation analysis for piecewise dynamical cycles is presented. Singular and regular perturbations are discussed, showing that if a simplified design system dynamics possess a stable attractor and if the fast (unmodeled) dynamics are asymptotically stable, then the asymptotic motion of the entire physical system is qualitatively similar to that of the design system. It is shown that simple, robust controllers can be designed to effectively control complex dynamical systems, where the desired behavior of the simple control design model is "passed along" to the realistic physical system for small enough perturbation parameters.