# 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));

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