nyquistfrequencybounds
======================

Computes the frequencies for which the nyquist locus enters and leaves
a given rectangle.



Calling Sequence
~~~~~~~~~~~~~~~~


::

    [fmin,fmax] = nyquistfrequencybounds(H,bounds)




Parameters
~~~~~~~~~~

:H A SISO linear dynamical system.
: :bounds A 2 by 2 array: [Rmin Imin;Rmax Imax] that defines a
  complex-plane rectangle.
: :fmin a real: the lowest frequency (Hz) such that the nyquist locus
  enters the given rectangle or 0 if the 0 Hz point lies in the
  rectangle or [] if the locus is completely outside the rectangle.
: :fmax a real: the highest frequency (Hz) such that the nyquist locus
  leaves the given rectangle or %inf if the %inf (hz) point is in the
  rectangle or [] if the locus is completely outside the rectangle.
:



Description
~~~~~~~~~~~

Given a C plane rectangle, `nyquistfrequencybounds` Computes the
lowest frequency for which the nyquist locus enters the rectangle and
the highest frequency for which the nyquist locus leaves the
rectangle.
This function is useful for high definition zoom of a nyquist locus.




Examples
~~~~~~~~


::

    s=%s
    num=2+9*s-9*s^2-11*s^3+0.01*s^4;
    den=43*s^2+65*s^3+34*s^4+8*s^5+s^6+0.1*s^7
    H=`syslin`_('c',num,den)-1  
    
    `clf`_;`set`_(`gcf`_(),'axes_size',[805,549])
    `subplot`_(221)
    `nyquist`_(H)
    
    
    `subplot`_(222)
    bounds=[-2 -2;2 2]
    [fmin,fmax]=nyquistfrequencybounds(H,bounds)
    `nyquist`_(H,fmin,fmax)
    `title`_("bounds:"+`sci2exp`_(bounds,0));
    
    `subplot`_(223)
    bounds=[-1.3 -0.3;0 0.3]
    [fmin,fmax]=nyquistfrequencybounds(H,bounds)
    `nyquist`_(H,fmin,fmax)
    `title`_("bounds:"+`sci2exp`_(bounds,0));
    
    `subplot`_(224)
    bounds=[-1.1 -0.1;-0.8 0.1]
    [fmin,fmax]=nyquistfrequencybounds(H,bounds)
    `nyquist`_(H,fmin,1d8)
    `title`_("bounds:"+`sci2exp`_(bounds,0));






See Also
~~~~~~~~


+ `nyquist`_


.. _nyquist: nyquist.html