## Chapter 42How To Run The Systems Package

The beginner should first print out the file NCDOCUMENT.doc which explains how to use NCAlgebra. A little practice with this would help.

To run SYSTEMS, enter

 math

at the UNIX prompt to execute Mathematica (or whatever command is appropriate for your non-UNIX system), followed by

 <

at the Mathematica

 In[1]:=

prompt.

That is all there is to it. Here SYStems.m loads NCAlgbra.m, one of the SYSTEMS DEFINITION files, plus two of the SYSTEMS UTILITY files described below.

These files are currently limited primarily to the study of H control of a certain class of nonlinear systems. There are additional files listed within comment delimiters in the SYSTEMS file which can be loaded to study slightly (but not much) different problems. This includes the option of studying so-called WIA systems in place of IA systems (see SYSHinf1 for definitions) or specializing to certain linear problems. A summary of files is given below. See the SYSTEMS file for further description.

The first time you run SYStem.s you should probably test to see that everything is in order. To do this you type:

 math  <

while ignoreing lots of stuff which scrolls by on the screen. What counts comes at the end. You should see a list which says Test1 is True, Test2 is True, etc.

Systems Definitions
 File                            Description  ---------------------------------------------------------------  SYSDef1PortLin.m    SYSDefIA.m      Loads the system definitions and hamiltonian                  for an Input-Affine system (see EXAMPLE 5.2)    SYSDefWIA.m     Definition of a WIA (W-Input-Affine) system                  SYSTEMS file could be edited to replace loading of                  SYSDef with loading of this file.    SYSDefWAccess.m    SYSDef2x2.m     Definition of two 2 ports and the coupling laws for                  coupling them as well as hamiltonians.

UTILITY FILES
 File                            Description  -----------      ---------------------------------------------------  SYSSpecialize.m  Rules for converting systems from nonlinear to                   linear, notation changes , etc.    SYSLinearize.m   Linearize system around 0 or around the                   diagonal x=z.  (We do not support this one)    SYSHinfFormulas.m   Formulas used in study of H-infinity control.    SYSHinf2x2Formulas.m   Formulas used in study of H-infinity control.

FILES CORRESPONDING TO RESEARCH ARTICLES
 File                            Description  -----------------------------------------------------------------  SYSHinfTAC.m An executable paper on nonlinear H-infinity control               together with rules to allow conversion to linear case.               Primarily for study of IA systems.