In this paper, the disturbance attenuation problem is formulated and solved for a class of linear hybrid systems in the presence of periodic jumps. The results are achieved, both in the finite and infinite horizon cases, by borrowing ideas from the theory of dynamic games. In the considered formulation, independent disturbances affecting the continuous-time and the discrete-time components of the hybrid system are allowed. Moreover, the analysis is carried out by introducing easily verifiable conditions, involving the definition of a Monodromy Riccati Equation , i.e., a classical Riccati equation defined for the one-period discrete-time equivalent model. Interestingly, as a by-product, the main statements essentially characterize the solution of zero-sum noncooperative dynamic games for periodic linear hybrid systems, which is of interest per se.

中文翻译：

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具有周期性跳跃的混合线性系统的 L2 增益：一种用于分析和设计的博弈论方法

在本文中，针对存在周期性跳跃的一类线性混合系统，制定并解决了扰动衰减问题。通过借鉴动态博弈理论的思想，在有限和无限视界情况下都获得了结果。在所考虑的公式中，允许影响混合系统的连续时间和离散时间分量的独立干扰。此外，分析是通过引入易于验证的条件进行的，包括 Monodromy Riccati 方程 的定义，即为单周期离散时间等效模型定义的经典 Riccati 方程。有趣的是，作为副产品，主要陈述本质上描述了周期线性混合系统的零和非合作动态博弈的解决方案，这本身就很有趣。