Controllability Gramian

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Zach
Zach 2011-7-26
编辑： Meena Farag 2016-6-1
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!

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Fangjun Jiang
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)
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Fangjun Jiang
Fangjun Jiang 2011-7-26
Sorry, I have no idea.
Meena Farag
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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