This paper presents a fundamental relation between Output Asymptotic Gains (OAG) and Input-to-Output Stability (IOS) gains for linear systems. For any Input-to-State Stable, strictly causal linear system the minimum OAG is equal to the minimum IOS-gain. Moreover, both quantities can be computed by solving a specific optimal control problem and by considering only periodic inputs. The result is valid for wide classes of linear systems (involving delay systems or systems described by PDEs). The characterization of the minimum IOS-gain is important because it allows the non-conservative computation of the IOS-gains, which can be used in a small-gain analysis. The paper also presents a number of cases for finite-dimensional linear systems, where exact computation of the minimum IOS gain can be performed.

中文翻译：

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线性系统IOS增益与渐近增益的关系

本文介绍了线性系统的输出渐近增益 (OAG) 和输入到输出稳定性 (IOS) 增益之间的基本关系。对于任何输入到状态稳定的严格因果线性系统，最小 OAG 等于最小 IOS 增益。此外，这两个量都可以通过解决特定的最优控制问题并仅考虑周期性输入来计算。结果适用于各种线性系统（包括延迟系统或 PDE 描述的系统）。最小 IOS 增益的表征很重要，因为它允许对 IOS 增益进行非保守计算，这可用于小增益分析。本文还介绍了一些有限维线性系统的情况，其中可以执行最小 IOS 增益的精确计算。