Function: ADD_DYN

Purpose. Introduces, in parallel to a given system, additional dynamics so that a dynamic feedback relative to the original system can be viewed as a proportional feedback relative to the extended system.

Synopsis.

sys1 = add_dyn(sys0,dyn);

[a1,b1,c1,d1] = add_dyn(a0,b0,c0,d0,dyn);

Description. If the original system sys0 corresponds to the state-space representation (A , B , C , D), (diag(dyn) is denoted Ω), the augmented system sys1 is given by

Applying the static feedback gain

to the above augmented system is equivalent to applying the following dynamic feedback

to (A , B , C , D).

This function must be used with dyn2sta and sta2dyn. This set of three functions permits the designer to tune dynamic feedback gains using fb_tun (which treats proportional feedback gains) or to design dynamic controllers using fb_prop (devoted to proportional gain design).

Alternatively, for the same purpose, the three functions add_dyn, dyn2sta, sta2dyn can be replaced by add_obs , dfb2obs, obs2dfb.

Input arguments.

`a0,b0,c0,d0` or `sys0`	Initial system.
`dyn`	Vector of additional dynamics without repetition of complex conjugate values.

Output arguments.

a1,b1,c1,d1 or sys1 Extended equivalent system.

See also: sta2dyn, dyn2sta