Controllability Gramian
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I have a system of the form xdot= Ax + Bu. I have my A and B matrix defined. But I'm having a bit of trouble using the controllability gramian. The syntax just says
Wc = gram(sys,'c') % controllability gramian
But I don't know how to define 'sys'. Any help? Thanks!
采纳的回答
Fangjun Jiang
2011-7-26
use the state space ss() function.
help ss
SS Constructs state-space model or converts model to state space.
Construction:
SYS = SS(A,B,C,D) creates an object SYS of class @ss representing
the continuous-time state-space model
dx/dt = Ax(t) + Bu(t)
y(t) = Cx(t) + Du(t)
3 个评论
Zach
2011-7-26
Fangjun Jiang
2011-7-26
Sorry, I have no idea.
Meena Farag
2016-6-1
编辑：Meena Farag
2016-6-1
I know this is several years late, but for anyone else reading this wondering the same thing, MATLAB 2016a has the option of computing the controllability gramian over some finite time. If your system is stable you can use the following:
opt = gramOptions('TimeInterval', [t0 tf]);
Wc = gram(sys,'c',opt);
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