Diagonal stability of a class of discrete‐time positive switched systems with delay. Issue 6 (1st February 2018)

• Record Type: Journal Article
• Authors: Aleksandrov, Alexander; Mason, Oliver
• Is Part Of: IET control theory & applications. Volume 12:Issue 6(2018)
• Page Start: 812
• Page End: 818
• Publication Date: 2018-02-01
• Subjects: stability -- discrete time systems -- nonlinear control systems -- delays -- Lyapunov methods -- linear matrix inequalities; diagonal stability -- discrete‐time positive switched systems -- discrete‐time nonlinear positive time‐delay switched systems -- sector‐type nonlinearities -- Lyapunov‐Krasovskii functionals -- linear algebraic inequalities -- digital filters -- neural networks; Control theory -- Periodicals; Automatic control -- Periodicals; 629.8312
• DOI: 10.1049/iet-cta.2017.1079
• Languages: English
• ISSNs: 1751-8644

Abstract

Abstract : A class of discrete‐time non‐linear positive time‐delay switched systems with sector‐type non‐linearities is studied. Sufficient conditions for the existence of common and switched diagonal Lyapunov–Krasovskii (L–K) functionals for this system class are derived; these are expressed as feasibility conditions for systems of linear algebraic inequalities. Corresponding spectral conditions for the existence of common L–K functionals are also described. Furthermore, it is shown that the proposed approaches can be applied to discrete‐time models of digital filters and neural networks. Finally, a numerical example is given to illustrate the effectiveness of theoretical results.