initial commit / add all books

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+//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;