//function// A=[-2 0;1 -1] B=[0;1] x=[0;0] disp(x,"x(t)=') s=poly(0,'s'); [Row Col]=size(A) //Size of a matrix A m=s*eye(Row,Col)-A //sI-A n=det(m) //To Find The Determinant of si-A p=inv(m) ; // To Find The Inverse Of sI-A syms t s m; disp(p,"phi(s)=") //Resolvent Matrix t=(t-m) q=eval(q) //At t=t-m ,evaluating q i.e phi(t-m) //Integrate q w.r.t m (Indefinite Integration) r=integ(q*B,m) m=0 //Upper limit is t g=eval(r) //Putting the value of upper limit in q m=t //Lower Limit is 0 h=eval(r) //Putting the value of lower limit in q y=(h-g); disp(y,"y=") printf("x(t)= phi(t)*x(0) + integ(phi(t-m)*B) w.r.t m from 0 t0 t \n") //x(t)=phi(t)*x(0)+integ(phi(t-m)*B)w.r.t m from 0 t0 t y1=(q*x)+y; disp(y1,"x(t)=") // CONTROLABILITY OF THE SYSTEM Cc=cont_mat(A,B); disp(Cc,"Controlability Matrix=") //To Check Whether the matrix(Cc)is singular i.e determint of Cc=0 if determ(Cc)==0; printf("Since the matrix is Singular, the system is not controllable \n"); else; printf("The system is controllable \n") end;