Compute upper bounds on Vinnicombe `gap`

and `nugap`

distances
between two systems

[gap,nugap] = gapmetric(p0,p1) [gap,nugap] = gapmetric(p0,p1,tol)

`[gap,nugap] = gapmetric(p0,p1)`

calculates upper bounds on the `gap`

and `nugap`

(Vinnicombe)
metric between systems `p0`

and `p1`

.
The `gap`

and `nugap`

values lie
between 0 and 1. A small value (relative to 1) implies that any controller
that stabilizes `p0`

will likely stabilize `p1`

,
and, moreover, that the closed-loop gains of the two closed-loop systems
will be similar. A `gap`

or `nugap`

of
0 implies that `p0`

equals `p1`

,
and a value of 1 implies that the plants are far apart. The input
and output dimensions of `p0`

and `p1`

must
be the same.

`[gap,nugap] = gapmetric(p0,p1,tol)`

specifies a relative accuracy for calculating the `gap`

metric
and `nugap`

metric. The default value for `tol`

is
0.001. The computed answers are guaranteed to satisfy

gap-tol < gapexact(p0,p1) <= gap

Georgiou, T.T., "On the computation of the gap metric,
" *Systems Control Letters,* Vol. 11, 1988,
p. 253-257

Georgiou, T.T., and M. Smith, "Optimal robustness in
the gap metric," *IEEE Transactions on Automatic Control,* Vol.
35, 1990, p. 673-686

Green, M., K. Glover, D. Limebeer, and J.C. Doyle, "A
J-spectral factorization approach to *H*_{∞} control," *SIAM
J. of Control and Opt.,* 28(6), 1990, p. 1350-1371

Qiu, L., and E.J. Davison, "Feedback stability under
simultaneous gap metric uncertainties in plant and controller," *Systems
Control Letters,* Vol. 18-1, 1992 p. 9-22

Vinnicombe, G., "Measuring Robustness of Feedback Systems," PhD Dissertation, Department of Engineering, University of Cambridge, 1993.

Zames, G., and El-Sakkary, "Unstable systems and feedback:
The gap metric," *Proceedings of the Allerton Conference,* October
1980, p. 380-385

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