Resize plot to fit text

Get the extent of the text objects after plotting the text.
Add the vertical position and height to get the upper position of each text object
Adjust the y axis limit so it contains all text objects.

h = text(1:numel(y),y,strsplit(num2str(y)),'VerticalAlignment','bottom');   
ext = cell2mat(get(h,'Extent'));                           % Step 1
upperPosition = sum(ext(:,[2,4]),2);                       % Step 2
ylim([min(ylim()),max(max(ylim()),max(upperPosition))])    % step 3

The y limit will be adjusted so that it maintains its current lower limit and increases its upper limit only if there is text that exceeds the axis boundaries.

Result

[update]

That could be reduced to one line where h is the handle to the text output.

ylim([min(ylim()), max(max(ylim()),max(cellfun(@(x)sum(x([2,4])),get(h,'Extent'))))])

It could also be put into an anonymous function where the two inputs are h and ax which are the text handles and the axis handle.

fitText = @(ax,h)ylim(ax,[min(ylim(ax)), max(max(ylim(ax)),max(cellfun(@(x)sum(x([2,4])),get(h,'Extent'))))]); 
fitText(gca,h)

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Adam Danz 2019-12-9

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The full code to produce the figure, text and y limits:

clf()
y = [1.6, 1.7, 2];
bar(y)
axis tight
h = text(1:numel(y),y,strsplit(num2str(y)),'VerticalAlignment','bottom');   
ext = cell2mat(get(h,'Extent'));                           % Step 1
upperPosition = sum(ext(:,[2,4]),2);                       % Step 2
ylim([min(ylim()),max(max(ylim()),max(upperPosition))])    % step 3