Qualitative equivalences of ISS and lp-gain stability properties for discrete-time nonlinear systems. (March 2017)

• Record Type: Journal Article
• Authors: Tran, Duc N.; Kellett, Christopher M.; Dower, Peter M.
• Is Part Of: Automatica. Volume 77(2017)
• Page Start: 360
• Page End: 369
• Publication Date: 2017-03
• Subjects: Input-to-state stability -- Discrete-time systems -- Nonlinear systems; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2016.11.033
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: Input-to-state stability (ISS) and input–output L 2 -gain are two important robust stability concepts in analyzing the interconnections of nonlinear dynamical systems. In this paper, we demonstrate several qualitative equivalences between different ISS related properties and l p -gain properties for discrete-time systems via nonlinear changes of coordinates. Prior to that, certain summation-to-summation estimates are shown to be equivalent to the standard definitions of ISS and integral ISS (iISS) which lead to sufficient Lyapunov function conditions to verify l p -gain properties. Combined with known results on the equivalence of 0 -input global asymptotic stability and iISS, and a superposition principle, we subsequently outline interesting implicative relationships between various discrete-time robust stability properties.