Diagonal stability of a class of discrete-time positive switched systems with delay
- Author(s): Alexander Aleksandrov 1, 2 and Oliver Mason 3, 4
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View affiliations
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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
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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/iet-cta.2017.1079 , Print ISSN 1751-8644, Online ISSN 1751-8652
© The Institution of Engineering and Technology
Received
28/09/2017,
Accepted
09/01/2018,
Revised
13/11/2017,
Published
09/01/2018
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.
Inspec keywords: stability; linear matrix inequalities; Lyapunov methods; discrete time systems; nonlinear control systems; delays
Other keywords: discrete-time positive switched systems; Lyapunov-Krasovskii functionals; discrete-time nonlinear positive time-delay switched systems; linear algebraic inequalities; neural networks; diagonal stability; digital filters; sector-type nonlinearities
Subjects: Discrete control systems; Distributed parameter control systems; Linear algebra (numerical analysis); Stability in control theory; Nonlinear control systems
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