I'm a little unclear about what you mean by "open". Figures don't really have "open" or "closed" states. They either exist or they don't. The FIGURE command will return a handle to the figure it makes:
hFig = figure(...your arguments here...);
You can also get a figure handle from the FINDOBJ function, which will find all graphics objects matching the property values you pass to it:
hFig = findobj(...your property/value pairs here...);
You can get rid of a figure with either of these commands:
close(hFig);
delete(hFig);
You can check if a figure has been closed/deleted using the function ISHANDLE:
ishandle(hFig) % Returns 'true' if the figure exists, 'false' if it doesn't
Figures can also be "visible" or "invisible". They have a 'Visible' property that you can get or set the value of:
get(hFig,'Visible') % Returns 'on' or 'off'
set(hFig,'Visible','off') % Makes a figure invisible,
% but it still exists (i.e. it's not closed)
If you're wanting to check if a figure is minimized, that may be a little more difficult. I believe there are some files that may help you with that on the MathWorks File Exchange: here's one to check out.