syslin
======

linear system definition



Calling Sequence
~~~~~~~~~~~~~~~~


::

    [sl]=syslin(dom,A,B,C [,D [,x0] ])
    [sl]=syslin(dom,N,D)
    [sl]=syslin(dom,H)




Arguments
~~~~~~~~~

:dom character string ( `'c'`, `'d'`), or `[]` or a scalar.
: :A,B,C,D matrices of the state-space representation ( `D` optional
  with default value zero matrix). For improper systems `D` is a
  polynomial matrix.
: :x0 vector (initial state; default value is `0`)
: :N, D polynomial matrices
: :H rational matrix or linear state space representation
: :sl tlist (" `syslin`" list) representing the linear system
:



Description
~~~~~~~~~~~

`syslin` defines a linear system as a list and checks consistency of
data.

`dom` specifies the time domain of the system and can have the
following values:

`dom='c'` for a continuous time system, `dom='d'` for a discrete time
system, `n` for a sampled system with sampling period `n` (in
seconds).

`dom=[]` if the time domain is undefined

State-space representation:


::

    sl=syslin(dom,A,B,C [,D [,x0] ])


represents the system :

The output of `syslin` is a list of the following form:
`sl=tlist(['lss','A','B','C','D','X0','dt'],A,B,C,D,x0,dom)` Note that
`D` is allowed to be a polynomial matrix (improper systems).

Transfer matrix representation:


::

    sl=syslin(dom,N,D) 
    sl=syslin(dom,H)


The output of `syslin` is a list of the following form : `sl =
rlist(N,D,dom)` or `sl=rlist(H(2),H(3),dom)`.

Linear systems defined as `syslin` can be manipulated as usual
matrices (concatenation, extraction, transpose, multiplication, etc)
both in state-space or transfer representation.

Most of state-space control functions receive a `syslin` list as input
instead of the four matrices defining the system.



Examples
~~~~~~~~


::

    A=[0,1;0,0];B=[1;1];C=[1,1];
    S1=syslin('c',A,B,C)   //Linear system definition
    S1("A")    //Display of A-matrix
    S1("X0"), S1("dt") // Display of X0 and time domain
    s=`poly`_(0,'s');
    D=s;
    S2=syslin('c',A,B,C,D)
    H1=(1+2*s)/s^2, S1bis=syslin('c',H1)
    H2=(1+2*s+s^3)/s^2, S2bis=syslin('c',H2)
    S1+S2
    [S1,S2]
    `ss2tf`_(S1)-S1bis
    S1bis+S2bis
    S1*S2bis
    `size`_(S1)




See Also
~~~~~~~~


+ `tlist`_ Scilab object and typed list definition.
+ `lsslist`_ Scilab linear state space function definition
+ `rlist`_ Scilab rational fraction function definition
+ `ssrand`_ random system generator
+ `ss2tf`_ conversion from state-space to transfer function
+ `tf2ss`_ transfer to state-space
+ `dscr`_ discretization of linear system
+ `abcd`_ state-space matrices


.. _dscr: dscr.html
.. _abcd: abcd.html
.. _ss2tf: ss2tf.html
.. _lsslist: lsslist.html
.. _ssrand: ssrand.html
.. _tf2ss: tf2ss.html
.. _tlist: tlist.html
.. _rlist: rlist.html