projsl

linear system projection

Calling Sequence

[slp]=projsl(sl,Q,M)

Arguments

:sl,slp syslin lists : :Q,M matrices (projection factorization) :

Description

slp`= projected model of `sl where Q*M is the full rank factorization of the projection.

If (A,B,C,D) is the representation of sl, the projected model is given by (M*A*Q,M*B,C*Q,D).

Usually, the projection Q*M is obtained as the spectral projection of an appropriate auxiliary matrix W e.g. W = product of (weighted) gramians or product of Riccati equations.

Examples

`rand`_('seed',0);sl=`ssrand`_(2,2,5);[A,B,C,D]=`abcd`_(sl);poles=`spec`_(A)
[Q,M]=`pbig`_(A,0,'c');  //keeping unstable poles
slred=projsl(sl,Q,M);`spec`_(slred('A'))
sl('D')=`rand`_(2,2);  //making proper system
`trzeros`_(sl)  //zeros of sl
wi=`inv`_(sl);  //wi=inverse in state-space
[q,m]=`psmall`_(wi('A'),2,'d');  //keeping small zeros (poles of wi) i.e. abs(z)<2
slred2=projsl(sl,q,m);
`trzeros`_(slred2)  //zeros of slred2 = small zeros of sl
//  Example keeping second order modes
A=`diag`_([-1,-2,-3]);
sl=`syslin`_('c',A,`rand`_(3,2),`rand`_(2,3));[nk2,W]=`hankelsv`_(sl)
[Q,M]=`pbig`_(W,nk2(2)-%eps,'c');    //keeping 2 eigenvalues of W
slr=projsl(sl,Q,M);  //reduced model
`hankelsv`_(slr)

See Also

• pbig eigen-projection