Detectability of Singularly Perturbed Systems

[摘要] A form of detectability, known as the input-output-to-statestability property, for singularly perturbed systems is examined in this work.This work extends the result of a paper by Christofides & Teel wherein they presenteda notion of total stability for input-to-state stability withrespect to singular perturbations.Analyzing singularly perturbed systems with outputs weshow that if the boundary layer system is uniformly globally asymptotically stable and the reduced system is input-output-to-state stablewith respect to disturbances, then these properties continue to hold, upto an arbitrarily small offset, for initial conditions in an arbitrarily large compact set and sufficiently small singular perturbation parameterover the time interval for which disturbances, theirderivatives, and outputs remain in an arbitrarily large compact set.An application of the result is presented where we analyze the stability of a circuit with a nonlinear element through the measurement of only one of the variables of interest.

[发布机构] University of Waterloo

[效力级别] IOSS

[关键词] Mathematics;IOSS;Singularly Perturbed Systems;Detectability