Construction of Periodic Counterexamples to the Discrete-Time Kalman Conjecture
Optimization and Control
2020-10-27 v1 Systems and Control
Systems and Control
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.
Keywords
Cite
@article{arxiv.2009.02468,
title = {Construction of Periodic Counterexamples to the Discrete-Time Kalman Conjecture},
author = {Peter Seiler and Joaquin Carrasco},
journal= {arXiv preprint arXiv:2009.02468},
year = {2020}
}
Comments
6 pages, 8 figures, submitted to IEEE CSL