This paper proposes a novel method to compute an upper bound on the induced L2- gain for a linear parameter varying (LPV) system with rational parameter dependence. The proposed method relies on a standard dissipation inequality condition. The storage function is a quadratic function of the state and a rational function of the parameters. The specific parameter dependence is restricted to involve (fixed) rational functions and an affine term with free decision variables. Finsler's lemma and affine annihilators are used to formulate sufficient linear matrix inequality (LMI) conditions for the dissipativity relation. The dimension and conservatism of the resulting LMI problem are reduced by the joint application of minimal generators and maximal annihilators. An LPV model of a pendulum-cart system is used to demonstrate the proposed method and compare it to existing techniques in the literature.

中文翻译：

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使用 Finsler 引理和最小生成器的有理 LPV 系统的诱导 L2 增益计算

本文提出了一种新方法，用于计算具有合理参数相关性的线性参数变化 (LPV) 系统的诱导 L2 增益的上限。所提出的方法依赖于标准耗散不等式条件。存储函数是状态的二次函数和参数的有理函数。特定的参数依赖仅限于涉及（固定的）有理函数和具有自由决策变量的仿射项。Finsler 引理和仿射湮灭器用于为耗散关系制定充分的线性矩阵不等式 (LMI) 条件。最小生成器和最大歼灭器的联合应用降低了由此产生的 LMI 问题的维度和保守性。