指数收敛速度的非因果FIR Zames-Falb乘子搜索
Noncausal FIR Zames-Falb Multiplier Search for Exponential Convergence Rate
摘要：
在现有文献中，有两种方法来估计稳定Lure系统的指数收敛速度的严格界。一方面，经典的积分二次约束（IQC）框架可以应用于回路变换，因此新回路的稳定性意味着原回路的收敛性。另一方面，可以修改IQC框架，即所谓的rho-IQC框架，使得在原始循环上直接获得收敛速度。在本技术说明中，我们将文献结果从寻找因果有限冲激响应（FIR）Zames-Falb乘法器扩展到非因果情况。我们证明了这两种方法的乘数是等价的变量变换。然而，Zames-Falb rho-IQC的因式分解与Zames-Falb IQC相比受到限制，因此提出了统一的因式分解。最后，数值例子表明，非因果乘数导致保守性较低的结果。
英文摘要：
In the existing literature, there are two approaches to estimate tighter bounds of the exponential convergence rate of stable Lure systems. On one hand, the classical integral quadratic constraint (IQC) framework can be applied under loop-transformation, so the stability of the new loop implies the convergence of the original loop. On the other hand, it is possible to modify the IQC framework, the so-called rho-IQC framework, in such a way that the convergence rate is directly obtained over the original loop. In this technical note, we extend the literature results from the search for a causal finite impulse response (FIR) Zames-Falb multiplier to the noncausal case. We show that the multipliers by the two approaches are equivalent by a change of variable. However, the factorisation of the Zames-Falb rho-IQC is restricted compared to the Zames-Falb IQC, so an unified factorisation is proposed. Finally, numerical examples illustrate that noncausal multipliers lead to less-conservative results.
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