Diagonal stability of a class of discretetime positive switched systems with delay
Diagonal stability of a class of discretetime positive switched systems with delay
 Author(s): Alexander Aleksandrov^{ 1, 2} and Oliver Mason^{ 3, 4}
 DOI: 10.1049/ietcta.2017.1079
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 Author(s): Alexander Aleksandrov^{ 1, 2} and Oliver Mason^{ 3, 4}


View affiliations

Affiliations:
1:
Faculty of Applied Mathematics and Control Processes , Saint Petersburg State University , Saint Petersburg 199034 , Russia ;
2: Department of Control of Complex Systems , ITMO University , Saint Petersburg 197101 , Russia ;
3: Department of Mathematics and Statistics/Hamilton Institute , Maynooth University , Co. Kildare , Ireland ;
4: Lero , The Irish Software Research Centre , Limerick , Ireland

Affiliations:
1:
Faculty of Applied Mathematics and Control Processes , Saint Petersburg State University , Saint Petersburg 199034 , Russia ;
 Source:
Volume 12, Issue 6,
17
April
2018,
p.
812 – 818
DOI: 10.1049/ietcta.2017.1079 , Print ISSN 17518644, Online ISSN 17518652
A class of discretetime nonlinear positive timedelay switched systems with sectortype nonlinearities 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 discretetime models of digital filters and neural networks. Finally, a numerical example is given to illustrate the effectiveness of theoretical results.
Inspec keywords: stability; linear matrix inequalities; Lyapunov methods; discrete time systems; nonlinear control systems; delays
Other keywords: discretetime positive switched systems; LyapunovKrasovskii functionals; discretetime nonlinear positive timedelay switched systems; linear algebraic inequalities; neural networks; diagonal stability; digital filters; sectortype nonlinearities
Subjects: Discrete control systems; Distributed parameter control systems; Linear algebra (numerical analysis); Stability in control theory; Nonlinear control systems
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