Interpolation and approximate feedback for an linear quadratic regulator (LQR) problem

The problem is to perform the following numerical experiment:

Suppose i have a second order controlled dynamical system:

And the performance index is

Next i have solved the system in MATLAB and found the state and control trajectories as follows:

clear all

close all

clc

x10=2;

x20=-3;

X0=[x10;x20];

A=[0 1;-2 1];

B=[0;1];

Q=[2 3;3 5];

R=[0.25];

[K,P,EV]=lqr(A,B,Q,R)

BIN=[0;0];

C= [1 1];

D= [1] ;

tfinal=10;

t=0:0.05:tfinal;

[Y,X,t]=initial(A-B*K,BIN,C,D,X0,t);

x1t=[1 0]*X';

x2t=[0 1]*X';

ut=-K*X' ;

figure(1)

plot(t,x1t, 'k' ,t,x2t, 'k'); grid on

xlabel ( 't' )

figure(2)

plot (t ,ut , ' k ' ); grid on

xlabel ('t')

The output i.e states and control is attached.

Now the question says : "make-believe" that you know the values of feedback only on a certain grid, construct such a grid by specifying 'h', and evaluate optimal feedback at those points only, and use some quasi interpolation to build approximate feedback for entire state space .

My queries are as follows:

(1) so here the gain , as far as i understand i need to grid the states x1(t) and x2(t) by some step size 'h' on a certain interval, and then evaluate the feedback and then use those values to interpolate, am i right?

(2) If this is right then how do i grid the data (x1,x2)? and interpolate ? i haven't solved this kind of problem in the past, so any help will be appreciated.