Function: DYN2STA

Purpose. Transforms a dynamic feedback relative to a system into an equivalent proportional gain relative to an extended system (extended by add_dyn).

Synopsis.

kprop = dyn2sta(fbdyn,dyn);

Description. With Ω = diag(dyn) and fbdyn corresponding to

the resulting gain kprop is of the form:

See add_dyn.

Input arguments

`fbdyn`	Dynamic feedback gain in LTI form (see `ss.m`).
`dyn`	Vector that is jointly used as input argument of `add_dyn`.

Output argument

kprop Equivalent proportional feedback.

See also: add_dyn, sta2dyn

Example. First, a dynamic LQG feedback gain fbdyn is designed relative to the system sys. Then, this dynamic gain is transformed using dyn2sta into a proportional feedback gain k1 relative to the extended system sysdyn obtained from sys using add_dyn.

System and feedback

   sys = rss(5,2,2); [a,b,c,d] = ssdata(sys);
   [ac,bc,cc,dc] = lqg(a,b,c,d,eye(7,7),eye(7,7));
   fbdyn = ss(ac,-bc,cc,-dc);

5th order dynamic extension

   dyn = [-1;-2+i;-2;-1];
   sysdyn = add_dyn(sys,dyn);
   k1 =  dyn2sta(fbdyn,dyn);

Results

   [eig_fb(sysdyn,k1) eig_fb(sys,fbdyn)

Both spectra are equal.