control.rar_control

disp('given matrix are :') A=[6 2 2 4 2 5;-9 -5 -3 -4 -3 -6;0 0 -3 0 0 0;-1 -1 -1 -3 -1 -1;9 6 3 4 4 6;-8 -2 -2 -4 -2 -7]; B=[0 -4 1 1;0 7 -1 -4;0 1 0 0;0 1 0 -1;1 -7 1 4;0 7 -1 -1]; C=[2 0 1 0 0 1;0 1 1 0 1 0;1 0 -4 0 0 1;0 -1 -4 4 0 1]; D=[0 0 1 2;0 4 6 7;0 0 1 0;3 0 0 0]; disp('A is :') disp(A) disp('B is :') disp(B) disp('C is :') disp(C) disp('D is :') disp(D) %finding eigenvalue and eigenvector disp('eigenvector and eigenvalue are :') [U,R]=eig(A) %finding Controllability disp('calculation of Controllability :') Co=ctrb(A,B) disp('finding rank of matrix Co :') rank(Co) disp('rank Co is 6') disp('Co is full rank') disp('system is controllable') %finding observability disp(' ') disp('***************') disp(' ') disp('calculation of observability :') Ob=obsv(A,C) disp('finding rank of matrix Ob :') rank(Ob) disp('rank Ob is 6') disp('Ob is full rank') disp('system is observable') disp('************************') disp(' ') disp('zero input response:') disp(' ') x0=[1;0;0;0;0;0]; t=0:0.1:1; sys=ss(A,[],C,[]); [y,t,x]=initial(sys,x0,t) disp(' ') disp('***********************') disp(' ') disp('calculation of e^A :') [V,D]=eig(A); exp_x=V*diag(exp(diag(D)))/V disp(' ') disp('*****************') disp(' ') disp(' calculation of transfer function : ') disp(' ') syms s I=eye(6) disp('s*I :') s*I disp('W=s*I-A :') W=s*I-A disp('F = inv(W):') F=inv(W) M=C*F*B disp(' H=transfer function :') D=[0 0 1 2;0 4 6 7;0 0 1 0;3 0 0 0]; M+D