linear system definition
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)
character string ('c'
,
'd'
), or []
or a
scalar.
matrices of the state-space representation
(D
optional with default value zero matrix). For
improper systems D
is a polynomial matrix.
vector (initial state; default value is
0
)
polynomial matrices
rational matrix or linear state space representation
tlist ("syslin
" list) representing the
linear system
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:
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:
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.
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) | ![]() | ![]() |