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- Title
The converging-input converging-state property for Lur'e systems.
- Authors
Bill, Adam; Guiver, Chris; Logemann, Hartmut; Townley, Stuart
- Abstract
Using methods from classical absolute stability theory, combined with recent results on input-to-state stability (ISS) of Lur'e systems, we derive necessary and sufficient conditions for a class of Lur'e systems to have the converging-input converging-state (CICS) property. In particular, we provide sufficient conditions for CICS which are reminiscent of the complex Aizerman conjecture and the circle criterion and connections are also made with small gain ISS theorems. The penultimate section of the paper is devoted to non-negative Lur'e systems which arise naturally in, for example, ecological and biochemical applications: the main result in this context is a sufficient criterion for a so-called 'quasi CICS' property for Lur'e systems which, when uncontrolled, admit two equilibria. The theory is illustrated with numerous examples.
- Subjects
STOCHASTIC convergence; STABILITY theory; EQUILIBRIUM; SMALL-gain theorem (Mathematics); LOGICAL prediction
- Publication
Mathematics of Control, Signals & Systems, 2017, Vol 29, Issue 1, p1
- ISSN
0932-4194
- Publication type
Article
- DOI
10.1007/s00498-016-0184-3