how to find steady state error of an arbitrary signal

I got a code which results a "y" signal as output and I wanted to find its steady state error. I gave an arbitrary input signal "W" as shown in my code

my code is as follows:

clc;
clear;
close all;
%% Initialization
T0=0 ;
Tf=20 ;
Ts=0.1 ;
t=T0:Ts:Tf ;
system=tf([1 1],[1 1 2]); % system=(s+1)/(s^2+s+2)
system_dis=c2d(system,Ts) ;
system_dis_ss=ss(system_dis) ;
Am=system_dis_ss.a;
Bm=system_dis_ss.b;
Cm=system_dis_ss.c;
n=size(Am,1); % Number of state variables
Om=zeros(1,n);
A=[Am,Om';Cm*Am,1];
B=[Bm ;Cm*Bm];
C=[Om 1];
p=10; % Prediction horizon
m=5; % Control horizon
Q=1;
R=1;
F=zeros(p,n+1);
for i=1:p
    F(i,:)=C*A^i;
end
PHI=zeros(p,m);
for i=1:p
    for j=1:i
        PHI(i,j)=C*A^(i-j)*B;
    end
end
PHI=PHI(:,1:m);
%% Main Loop
Nt=numel(t);
%W=ones(Nt,1); % Reference signal
W=[ones(floor(Nt/4),1);2*ones(floor(Nt/4),1);-ones(floor(Nt/4),1);zeros(floor(Nt/4+1),1)];
y=zeros(Nt,1);
du=zeros(Nt,1);
x=zeros(n+1,Nt); % (System state)+integral ===> n+1
Fval=zeros(Nt,1);
for i=1:Nt-1
    FreeResponse=F*x(:,i);
    dU=(PHI'*Q*PHI+R)\(PHI'*Q*(W(i)-FreeResponse)) ;
    du(i)=dU(1); % Receding horizon
    x(:,i+1)=A*x(:,i)+B*du(i); % State variable update
    y(i+1)=C*x(:,i+1); % Output update
end
%%
ynew=y(21:101);
Wnew=W(21:101);
Mp=100*(max(ynew)/ynew(81,1))
figure(1)
plot(t(21:101),y(21:101),'linewidth',2)

[Aquatris]

Steady state error is when the difference between the output and the desired value of the output when the output does not change anymore.

Numerically you can apply an input to your system, run you system long enough for output of the system to settle at a constant value. Then compare the output value to the desired value to obtain the steady state error.

Alternatively, since you have your system, you can use stepinfo function to obtain the answer.

However your system seems to be an unstable one, which makes no sense to define steady state error.

[Ali Esmaeilpour]

my system is stable. plz give me a code I don't want definition of ess.