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ss2ss
state-space to state-space conversion, feedback, injection
Syntax
[Sl1,right,left]=ss2ss(Sl,T, [F, [G , [flag]]])
Arguments
- Sl
linear system (
syslin
list) in state-space form- T
square (non-singular) matrix
- Sl1, right, left
linear systems (syslin lists) in state-space form
- F
real matrix (state feedback gain)
- G
real matrix (output injection gain)
Description
Returns the linear system Sl1=[A1,B1,C1,D1]
where
A1=inv(T)*A*T, B1=inv(T)*B, C1=C*T, D1=D
.
Optional parameters F
and G
are state feedback and output injection respectively.
For example, Sl1=ss2ss(Sl,T,F)
returns
Sl1
with:
and right
is a non singular linear system such
that Sl1=Sl*right
.
Sl1*inv(right)
is a factorization of
Sl
.
Sl1=ss2ss(Sl,T,0*F,G)
returns
Sl1
with:
and left
is a non singular linear system such
that Sl1=left*Sl
(right=Id
if
F=0
).
When both F
and G
are given,
Sl1=left*Sl*right
.
When
flag
is used andflag=1
an output injection as follows is usedand then a feedback is performed,
F
must be of size(m+p,n)
right
andleft
have the following property:When
flag
is used andflag=2
a feedback (F
must be of size(m,n)
) is performed and then the above output injection is applied.right
andleft
have the following property:
Examples
Sl=ssrand(2,2,5); trzeros(Sl) // zeros are invariant: Sl1=ss2ss(Sl,rand(5,5),rand(2,5),rand(5,2)); trzeros(Sl1), trzeros(rand(2,2)*Sl1*rand(2,2)) // output injection [ A + GC, (B+GD,-G)] // [ C , (D , 0)] p=1,m=2,n=2; sys=ssrand(p,m,n); // feedback (m,n) first and then output injection. F1=rand(m,n); G=rand(n,p); [sys1,right,left]=ss2ss(sys,rand(n,n),F1,G,2); // Sl1 equiv left*sysdiag(sys*right,eye(p,p))) res=clean(ss2tf(sys1) - ss2tf(left*sysdiag(sys*right,eye(p,p)))) // output injection then feedback (m+p,n) F2=rand(p,n); F=[F1;F2]; [sys2,right,left]=ss2ss(sys,rand(n,n),F,G,1); // Sl1 equiv left*sysdiag(sys,eye(p,p))*right res=clean(ss2tf(sys2)-ss2tf(left*sysdiag(sys,eye(p,p))*right)) // when F2= 0; sys1 and sys2 are the same F2=0*rand(p,n);F=[F1;F2]; [sys2,right,left]=ss2ss(sys,rand(n,n),F,G,1); res=clean(ss2tf(sys2)-ss2tf(sys1))
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