Zames-Falb multipliers for MIMO nonlinearities
Zames-Falb multipliers for MIMO nonlinearities
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用于 MIMO 非线性的 Zames-Falb 乘法器
DOI：
10.1109/acc.2000.877001
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发表时间：
2000
期刊：
影响因子：
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通讯作者：
V. Kulkarni
中科院分区：
文献类型：
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作者：
M. Safonov;V. Kulkarni
Zames和Falb(1968)确定了一类保持单调SISO非线性正性的乘子。他们推测，他们的结果可能也适用于增量正的、范数有界的MIMO非线性。在这篇文章中，我们证明了他们关于MIMO非线性的猜想只有在施加进一步的限制时才成立。具体地说，我们证明了将非线性项限制为凸实函数的梯度或将乘子限制为频率的实值函数就足够了。
Zames and Falb (1968) determined a class of multipliers that preserve positivity of monotone SISO nonlinearities. They conjectured that their results might also hold for incrementally positive, norm-bounded MIMO nonlinearities. In this note, we demonstrate that their conjecture regarding MIMO nonlinearities holds true only if a further restriction is applied. Specifically, we show that it suffices either to restrict the nonlinearity to be the gradient of a convex real-valued function or to restrict the multiplier to be a real-valued function of frequency.