An ISS characterization for discontinuous discrete‐time systems. Issue 1 (18th November 2019)

• Record Type: Journal Article
• Authors: Geiselhart, R.; Noroozi, N.
• Other Names: Eberhardsteiner J. guestEditor.; Schöberl M. guestEditor.
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 19:Issue 1(2019)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2019-11-18
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201900121
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: Input‐to‐state stability (ISS) is an important concept to study robustness properties of nonlinear control systems. The ISS property can be, in particular, characterized by ISS Lyapunov functions. For discrete‐time nonlinear control systems two different forms of ISS Lyapunov functions (implication‐form and dissipation‐form) are known to be equivalent if the dynamics are continuous. However, for discontinuous dynamics the equivalence is no longer satisfied. In this work, we discuss this phenomenon and, eventually, give a complete characterization of ISS in terms of ISS Lyapunov functions.