Multivariate positive functions under coefficient perturbation

Testing of positive realness of a rational function when its coefficients vary over given intervals is required in practical applications such as design of adaptive control systems. The k-variate positive function is first related to a (k+1)-variate Hurwitz polynomial. Then, using the Kharitonov-type results for Hurwitz polynomials, similar results are derived for multivariate positive functions and multivariate very strict positive functions. This derivation shows that for a k-variate interval positive function, only 8*2/sup k/ extremum positive functions need be tested. This is against the previously reported 16*4/sup k/ functions for the multivariate case and 32 for the single-variate case. The interval positive real functions require the testing of 4*2/sup k/ extremum functions.<
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