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# syslin

linear system definition

### Syntax

[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

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