Section: Software
RARL2
Participants : JeanPaul Marmorat, Martine Olivi [ corresponding participant ] .
RARL2 (Réalisation interne et Approximation Rationnelle L2) is a software for rational approximation (see section 3.1.4 ) http://wwwsop.inria.fr/apics/RARL2/rarl2eng.html .
This software takes as input a stable transfer function of a discrete time system represented by

either its internal realization,

or its first N Fourier coefficients,

or discretized values on the circle.
It computes a local best approximant which is stable, of prescribed McMillan degree , in the L^{2} norm.
It is akin to the arl2 function of Endymion (see section 5.5 ) from which it differs mainly in the way systems are represented: a polynomial representation is used in Endymion, while RARL2 uses realizations, this being very interesting in certain cases. It is implemented in Matlab. This software handles multivariable systems (with several inputs and several outputs), and uses a parametrization that has the following advantages

it incorporates the stability requirement in a builtin manner,

it allows the use of differential tools,

it is wellconditioned, and computationally cheap.
An iterative research strategy on the degree of the local minima, similar in principle to that of arl2, increases the chance of obtaining the absolute minimum (see section 6.4 ) by generating, in a structured manner, several initial conditions.
RARL2 performs the rational approximation step in our applications to filter identification (section 4.3 ) as well as sources or cracks recovery (section 4.2 ). It was released to the universities of Delft, Maastricht, Cork and Brussels. The parametrization embodied in RARL2 was recently used for a multiobjective control synthesis problem provided by ESTECESA, The Netherlands (section 6.4 ). An extension of the software to the case of triple poles approximants is now available. It gives nice results in the source recovery problem (section 6.3.2 ). It is used by FindSources3D (see 5.7 ).