syslin linear system definition

## Syntax

                 sl = syslin(dom, A, B, C)
                 sl = syslin(dom, A, B, C, D)
                 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

s.X | = A.X + B.u
y | = C.X + D.u
x(0) | = x0

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
- lsslist
- rlist
- ssrand
- ss2tf
- tf2ss
- dscr
- abcd