Equivalence between uniform- and varying-sampling stability properties for discrete-time exact and approximate models

ALEXIS J. VALLARELLA; ESTEBAN N. OSELLA; HERNAN HAIMOVICH

Mar del Plata

Workshop; Information Processing and Control (RPIC), 2017 XVII Workshop on; 2017

Digital control strategies for continuous-time (CT)nonlinear systems often face the problem of determining anappropriate discrete-time (DT) model. The exact DT model forthe nonlinear system is unavailable in general, and thus approximatemodels must be employed for control design. Conditionsthat ensure practical stability of the exact DT model for allsufficiently small sampling periods based on the stability ofthe approximate model exist in the literature. Most of theseexisting results assume that the sampling period is kept constantduring operation, and show that stability holds if the samplingperiod is small enough. Since such results may be not valid ina varying sampling rate (VSR) setting, previous work focusedon a suitable extension, specifically aimed at controller-drivensampling (CDS). In this paper, we show that a specific stabilityproperty named (β, Rn)-stability, and its CDS extension, named(β, Rn)-stability under VSR, are equivalent. The equivalence ofthese two properties is not trivial, in the sense that it cannotbe deduced directly from their definitions. We also provide an-δ characterization of (β, Rn)-stability under VSR which maybe useful in establishing the equivalence between other stabilityproperties and their corresponding CDS extensions.