Conference Proceedings

Equivalences of Stability Properties for Discrete-Time Nonlinear Systems

DN Tran, CM Kellett, PM Dower, A Bobtsov, S Kolyubin, A Pyrkin

IFAC-PapersOnLine | Elsevier | Published : 2015


Abstract Several qualitative equivalences are demonstrated between various robust stability properties for discrete-time nonlinear systems. In particular, two different summation-to-summation estimates are shown to be equivalent to the standard definitions of Input-to-State Stability (ISS) and integral ISS (iISS), respectively. Furthermore, ISS and iISS are shown to be qualitatively equivalent, via a nonlinear change of coordinates, to linear and nonlinear l2-gain properties, respectively. These equivalences, together with a previous result on the equivalence of 0-input global asymptotic stability and iISS provide interesting relationships between discrete-time robust stability properties th..

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