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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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