RARL2

How does it work ?

Note that RARL2 requires the presence of the OPTIM and CONTROL toolboxes in order to work.
The routines have been coded with Matlab 6.5. and can therefore run under this version of Matlab.

You may download the users guide

The problem
The method
The data
Tutorial

The problem

The method

The data

Tutorial

Content of the directory trunk

• boplib: the routines for a parametrization of stable allpass systems by means of balanced observable pairs
• arl2lib: the routines for the use of "bop" parametrization for L2 rational approximation. Contains the functions arl2.m and rarl2.m which perform rational approximation from user data.
• demos: a selection of benchmarks and random systems approximations.
• data: contain the '.mat' files of some data.
• bopDEMO.m run the demos.

To handle your own data, you may use the functions arl2.m or RARL2.m
Systems and data must be in dicrete-time.

First add the required path:

arl2.m

• Enter the data structure.
  data: '.mat file' which contains a matlab structure 'userData'
  • userData.type is 'sys', 'coeff' or 'sample'
  • userData.value according to the data type
  You may for example load one of the '.mat' file available in the directory 'data'. For example load the system HB61 :
  
• Specify the arl2_options:
  
  • 'type'= real or complex (real if the system is real i.e. conjugate symmetric)
  • 'mode'= mono or triple (triple if triple pole approximants are searched)
  
  
  
• Enter an initial system, i.e. an ss matlab structure 'sys0'.
  Can be a random initial system or an initial system obtained by another method (AAK..)
  
  
  
• specify optim_option, the options of the matlab function 'fmincon'.
  
  

RARL2.m

RARL2 recursively runs arl2: when processing degree k+1, a number of maxIP x p initial guesses are built from the best k-degreed order approximant to arl2.

• n: approximant degree
• maxIP: number of initial points; default is 2 in the case 'real' and 4 in the case 'complex'