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# nyquistfrequencybounds

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

### Syntax

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

### Parameters

- H
A SISO or SIMO linear dynamical system, in state space, transfer function or zpk representations, in continuous or discrete time.

- 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.

### 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

### History

Version | Description |

6.0 | handling zpk representation |

## Comments

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