syslin - Linear system definition (original) (raw)

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 is0)

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 periodn (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=tlist(['r','num','den','dt'],N,D,dom) orsl=tlist(['r','num','den','dt'],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 asyslin 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)
S1("A")
S1("X0"), S1("dt") s=poly(0,'s'); D=s; S2=syslin('c',A,B,C,D) H1=(1+2s)/s^2, S1bis=syslin('c',H1) H2=(1+2s+s^3)/s^2, S2bis=syslin('c',H2) S1+S2 [S1,S2] ss2tf(S1)-S1bis S1bis+S2bis S1*S2bis size(S1)