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    %% Sampling ultidyn Elements
% When sampling an |ultidyn| element or an uncertain object that contains a
% |ultidyn| element, the result is always a state-space (|ss|) object. The
% property |SampleStateDimension| of the |ultidyn| class determines the state
% dimension of the samples.
%%
% Create a 1-by-1, gain bounded |ultidyn| object with gain bound 3. Verify
% that the default state dimension for samples is 1.

% Copyright 2015 The MathWorks, Inc.

del = ultidyn('del',[1 1],'Bound',3); 
del.SampleStateDimension 
%%
% Sample the uncertain element at 30 points. Verify that this creates a
% 30-by-1 |ss| array of 1-input, 1-output, 1-state systems. 
delS = usample(del,30); 
size(delS) 
%%
% Plot the Nyquist plot of these samples and add a disk of radius 3. Note
% that the gain bound is satisfied and that the Nyquist plots are all
% circles, indicative of 1st order systems.
nyquist(delS) 
hold on; 
theta = linspace(-pi,pi); 
plot(del.Bound*exp(sqrt(-1)*theta),'r'); 
hold off; 
%%
% Change |SampleStateDimension| to 4, and repeat entire procedure. The
% Nyquist plots satisfy the gain bound and as expected are more complex
% than the circles found in the 1st-order sampling.
del.SampleStateDimension = 4; 
delS = usample(del,30);   
nyquist(delS) 
hold on; 
theta = linspace(-pi,pi); 
plot(del.Bound*exp(sqrt(-1)*theta),'r'); 
hold off;