Induced L2-gain computation for rational LPV systems using Finsler\u27s lemma and minimal generators

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. Thestorage function is a quadratic function of the state and a rational function of theparameters. The specific parameter dependence is restricted to involve (fixed) rationalfunctions and an affine term with free decision variables. Finsler\u27s lemma and affineannihilators are used to formulate sufficient linear matrix inequality (LMI) conditions forthe dissipativity relation. The dimension and conservatism of the resulting LMI problemare reduced by the joint application of minimal generators and maximal annihilators. AnLPV model of a pendulum-cart system is used to demonstrate the proposed methodand compare it to existing techniques in the literature