Induced L2-gain computation for rational LPV systems using Finsler's lemma and minimal generators
Journal article, 2020

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.

induced L2 gain

linear fractional transformation

rational Lyapunov function

Linear parameter varying systems



Peter Polcz

Pázmány Péter Catholic University

Tamas Peni

Hungarian Academy of Sciences

Balázs Adam Kulcsár

Chalmers, Electrical Engineering, Systems and control, Automatic Control

Gabor Szederkenyi

Pázmány Péter Catholic University

Hungarian Academy of Sciences

Systems and Control Letters

0167-6911 (ISSN)

Vol. 142 104738

OPerational Network Energy managemenT for electrified buses (OPNET)

Swedish Energy Agency, 2018-10-01 -- 2021-12-31.

Areas of Advance


Subject Categories

Computational Mathematics


Control Engineering



More information

Latest update