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arXiv · 2009.02468

Construction of Periodic Counterexamples to the Discrete-Time Kalman Conjecture

Peter Seiler·Joaquin Carrasco
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Abstract

This paper considers the Lurye system of a discrete-time, linear time-invariant plant in negative feedback with a nonlinearity. Both monotone and slope-restricted nonlinearities are considered. The main result is a procedure to construct destabilizing nonlinearities for the Lurye system. If the plant satisfies a certain phase condition then a monotone nonlinearity can be constructed so that the Lurye system has a non-trivial periodic cycle. Several examples are provided to demonstrate the construction. This represents a contribution for absolute stability analysis since the constructed nonlinearity provides a less conservative upper bound than existing bounds in the literature.

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BibTeXRIS

Peter Seiler, Joaquin Carrasco. 2020-09-05. Construction of Periodic Counterexamples to the Discrete-Time Kalman Conjecture. https://doi.org/10.1109/lcsys.2020.3033443

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