离散时间Kalman猜想周期反例的构造
Construction of Periodic Counterexamples to the Discrete-Time Kalman Conjecture
摘要：
本文研究了具有非线性负反馈的离散线性定常对象的Lurye系统。单调和斜率限制的非线性。主要结果是一个程序来构建不稳定的非线性Lurye系统。如果被控对象满足一定的相位条件，则可以构造单调非线性，使得Lurye系统具有非平凡的周期循环。提供了几个例子来演示该结构。这代表了对A稳定性分析的贡献，因为构造的非线性提供了比文献中现有界限更不保守的上界。
英文摘要：
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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