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Diagonal Lyapunov–Krasovskii functionals for discrete-time positive systems with delay

Authors
Journal
Systems & Control Letters
0167-6911
Publisher
Elsevier
Volume
63
Identifiers
DOI: 10.1016/j.sysconle.2013.10.012
Keywords
  • Positive Systems
  • Delay
  • Stability
  • Diagonal Lyapunov–Krasovskii Functional

Abstract

Abstract We consider the existence of diagonal Lyapunov–Krasovskii (L–K) functionals for positive discrete-time systems subject to time-delay. In particular, we show that the existence of a diagonal functional is necessary and sufficient for delay-independent stability of a positive linear time-delay system. We extend this result and provide conditions for the existence of diagonal L–K functionals for classes of nonlinear positive time-delay systems, which are not necessarily order preserving. We also describe sufficient conditions for the existence of common diagonal L–K functionals for switched positive systems subject to time-delay.

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