论文标题
为离散时间Kalman猜想构建定期反例
Construction of Periodic Counterexamples to the Discrete-Time Kalman Conjecture
论文作者
论文摘要
本文考虑了以非线性为负反馈的离散时间，线性时间不变的工厂的Lurye系统。都考虑了单调和斜率限制的非线性。主要结果是为Lurye系统构建不稳定的非线性的程序。如果植物满足特定相条件，则可以构建单调非线性，以使Lurye系统具有非平凡的周期性周期。提供了几个示例来证明构造。这代表了绝对稳定性分析的贡献，因为构造的非线性比文献中的现有界限提供了不太保守的上限。
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.
