discrete time response (state space)
[X]=ltitr(A,B,U,[x0])
[xf,X]=ltitr(A,B,U,[x0])
:A,B real matrices of appropriate dimensions : :U,X real matrices : :x0,xf real vectors (default value=0 for x0)) :
calculates the time response of the discrete time system
x[t+1] = Ax[t] + Bu[t].
The inputs ui‘s are the columns of the U matrix
U=[u0,u1,...,un];
x0 is the vector of initial state (default value : 0) ;
X is the matrix of outputs (same number of columns as U).
X=[x0,x1,x2,...,xn]
xf is the vector of final state xf=X[n+1]
A=`eye`_(2,2);B=[1;1];
x0=[-1;-2];
u=[1,2,3,4,5];
x=ltitr(A,B,u,x0)
x1=A*x0+B*u(1)
x2=A*x1+B*u(2)
x3=A*x2+B*u(3) //....