%LTSOB Loop transfer function for an observer based tracking system.
% LTSOB is a script that calculates a state-space description
% of the loop transfer function for an observer based
% tracking system. Such a tracking system can be designed using
% the functions DTS and FBG.
%
% INPUTS:
%
% phi,gamma ZOH equivalent plant model.
% c Output matrix, y[k]=c*x[k]
% K Observer gains matrix
% phia,gammaa State space matrices for additional dynamics
% L1,L2 Feedback gains for cascade of plant and additional
% dynamics.
%
% OUTPUTS:
%
% phi_L,gamma_L,c_L State-space description of loop transfer function.
%
% To find stability margins, use SM(phi_L,gamma_L,c_L).
% R.J. Vaccaro 12/97,11/98
[nn_1,nn_2]=size(gamma);
nn_3=length(phia);
phi_L=[phi zeros(nn_1,nn_1+nn_3);...
K*c phi-K*c-gamma*L1 -gamma*L2;...
gammaa*c zeros(nn_3,nn_1) phia];
gamma_L=[gamma;zeros(nn_1+nn_3,length(gamma(1,:)))];
c_L= [zeros(nn_2,nn_1) L1 L2];
clear nn_1 nn_2 nn_3
sm(phi_L,gamma_L,c_L)
