Passivity analysis of rational LPV systems using Finsler's lemma

Paper in proceeding, 2019

An optimization based systematic passivity analysis procedure and an output projection is proposed in this paper for asymptotically stable linear parameter varying (LPV) systems in the linear fractional representation (LFR) form having at least as many independent output signals as input
signals. The storage function is searched in a quadratic form with a symmetric rational parameter dependent matrix. In order to form a square system and then to satisfy the Kalman-Yakubovich-Popov (KYP) properties, a parameter dependent output projection matrix is searched in the LFR form. The nonlinear parameter dependence from the linear matrix inequality (LMI) and equality (LME) conditions provided by the KYP lemma is factorized out using the linear fractional transformation(LFT). Then, Finsler’s lemma and affine annihilators are used to relax the sufficient affine parameter dependent LMI and LME conditions. As an application example, stable system inversion is addressed and demonstrated on a benchmark rational LPV model.