Induced L2-gain computation for rational LPV systems using Finsler's 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. 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.