fig39.m

realize analysis and design for computer-controlled system

% Generates Fig 3.9
% Computer Controlled Systems (3rd ed)
% Author: B. Wittenmark
% Last edit: 1997-07-27
% Copyright (c) 1996 by K. J. 舠tr鰉, B. Wittenmark and
% Department of Automatic Control, Lund Institute of
% Technology, Lund, Sweden

newplot;clf
set(gcf,'PaperUnits','centimeters','PaperPosition',[2 2 13 8])
set(gcf,'Units','centimeters','position',get(gcf,'PaperPosition'))

lw=0.9;
Ms=9;

a=[0.4 0; -0.4 0.6];
N=6;
x=zeros(2,N);
x(:,1)=[2 ;-1];
for i=1:N, x(:,i+1)=a*x(:,i); end;
hpl=plot(x(1,:),x(2,:),'k--',x(1,:),x(2,:),'k.','Linew',lw);
set(hpl,'MarkerSize',Ms)
axis('equal')
axis([-3 3 -2 2])
set(gca,'Fontsize',9,'Fontname','NewCenturySchlbk');
set(gca,'xtick',[-2 0 2],'ytick',[-2 0 2]);
xlabel('State \it{x}_1','fontname','NewCenturySchlbk','fontsize',9)
ylabel('State \it{x}_2','fontname','NewCenturySchlbk','fontsize',9)
hold on

x=zeros(2,N);
x(:,1)=[2 ;1];
for i=1:N, x(:,i+1)=a*x(:,i); end;
hpl=plot(x(1,:),x(2,:),'k--',x(1,:),x(2,:),'k.','Linew',lw);
set(hpl,'MarkerSize',Ms)
hold on

x=zeros(2,N);
x(:,1)=[1 ;2];
for i=1:N, x(:,i+1)=a*x(:,i); end;
hpl=plot(x(1,:),x(2,:),'k--',x(1,:),x(2,:),'k.','Linew',lw);
set(hpl,'MarkerSize',Ms)
hold on

x=zeros(2,N);
x(:,1)=[-1 ;2];
for i=1:N, x(:,i+1)=a*x(:,i); end;
hpl=plot(x(1,:),x(2,:),'k--',x(1,:),x(2,:),'k.','Linew',lw);
set(hpl,'MarkerSize',Ms)
hold on

x=zeros(2,N);
x(:,1)=[-2 ;-1];
for i=1:N, x(:,i+1)=a*x(:,i); end;
hpl=plot(x(1,:),x(2,:),'k--',x(1,:),x(2,:),'k.','Linew',lw);
set(hpl,'MarkerSize',Ms)

x=zeros(2,N);
x(:,1)=[-1 ;-2];
for i=1:N, x(:,i+1)=a*x(:,i); end;
hpl=plot(x(1,:),x(2,:),'k--',x(1,:),x(2,:),'k.','Linew',lw);
set(hpl,'MarkerSize',Ms)

q=[1 0;0 1];
p=dlyap(a,q);

for i=1:51;
for j=1:51;
x1=-2.5+0.1*(i-1);
x2=-2.5+0.1*(j-1);
v(i,j)=[x1 x2]*p*[x1;x2];end;end;
x1=-2.5:0.1:2.5;
x2=-2.5:0.1:2.5;
contour(x1,x2,v,[0.1  0.5 2 5 10 ],'k-')

plot([-3 3],[0 0],'k:')
plot([0 0],[-2 2],'k:')