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+//Example 7.25
+// An estimator design for a simple pendulum
+
+xdel(winsid())//close all graphics Windows
+clear;
+clc;
+//------------------------------------------------------------------
+// State space representation
+w0=1;
+F=[0 1; -w0^2 0];
+G=[0 1]';
+H=[1 0];
+J=0;
+n=sqrt(length(F));//order of the system
+// Desired estimator poles
+Pe=[-10*w0 -10*w0];
+// Observer gain matrix for system 
+Lt=ppol(F',H',Pe);
+L=Lt';
+disp(L,"L=" );
+//------------------------------------------------------------------
+//simulation for closed loop system
+x0=[1 0]' //initial condition
+
+//State feedback control law u=-Kx; (from Ex7_15)
+K=[3*w0^2 4*w0];
+//------------------------------------------------------------------
+//Augmented plant and observer
+Faug=[F-G*K, zeros(n,n); L*H, F-L*H];
+Gaug=[0 0 0 0]';
+Haug=[H -H];
+Jaug=0;
+
+sys_aug=syslin('c',Faug,Gaug,Haug,Jaug);
+t=0:0.1:4;
+u=zeros(1,length(t));
+x0=[1 0 0 0]';
+[x z]=csim(u,t,sys_aug,x0); //closed loop response
+plot(t,z(1,:));
+plot(t,z(2,:),'m');
+plot(t,z(3,:),'b:');
+plot(t,z(4,:),'m:');
+
+//Title, labels and grid to the figure
+exec .\fig_settings.sci; // custom script for setting figure properties
+title(['Initial condition response of oscillator showing',...
+'$\mathbf{x}$','and','$\hat{\mathbf{x}}$'],'fontsize',3)
+xlabel('Time t (sec.)','fontsize',2)
+ylabel('Amplitude','fontsize',2)
+legend('$x_1$','$x_2$','$\hat{x}_1$','$\hat{x}_2$')
+xset('font size',2)
+//------------------------------------------------------------------