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How can I analyze the stabilizability and the detectability of linear invariant discrete system

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ZATLA Hicham
ZATLA Hicham 2015-6-16
评论： Zakaria BACHIR 2016-11-14
I have a linear discrete systeme with big matrix for example A(100x100) and I want to analyze the stabilizability and the detectability for my linear system can you help me please?
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Nshine
Nshine 2016-6-27
I am working through the same problem. For what its worth, regarding Stabilizability, the Matlab function
[GS,GNS] = stabsep(G)
decomposes G into stable and unstable parts.
You can then check the controllability of the unstable part.
if G is a state-space model, if
rank(ctrb(GNS.a,GNS.b)) = size(GNS.a,1)
then the unstable modes are controllable. if
rank(ctrb(GNS.a,GNS.b)) < size(GNS.a,1)
then the some or all of these modes are uncontrollable.
You can probably use a similar method for the detectability of the unstable modes, but I haven't tried it.
I'm interested if anyone has a better solution
Zakaria BACHIR
Zakaria BACHIR 2016-11-14
@Nshine What if G is a transfer function
[num,den] = ss2tf(A,B,C,D,1);
G = tf(num(1),den)
[GS,GNS] = stabsep(G) %Gs for stable part, GNS for unstable part
rank(ctrb(GNS.A,GNS.B)) = size(GNS.A,1)
rank(ctrb(GNS.A,GNS.B)) < size(GNS.A,1)
In this case there is an eroor showing that :
*No property of the class "tf" matches the string "A". Use PROPERTIES to get the list of
properties for this class.*

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