ON THE STABILITY OF INTERVAL FAMILIES OF CHARACTERISTIC FUNCTIONS DEPENDING LINEARLY ON PARAMETERS

[摘要] We consider a parametric family F := {f(p)(z) : p is an element of P} of functions f(p)(z) holomorphic in a closed region D subset of C depending continuously on a finite dimensional real or complex parameter vector p := (p(1), p(2),..., p(n)) ranging over a closed region P in parameter space. The problem is to establish criteria which guarantee that f(p)(z) not equal 0 for z is an element of D and p is an element of P. Such criteria are needed in order to reduce the amount of checks to be performed when verifying classwise stability. In the case of linear parameter dependence, f(p)(z) := f(0)(z) + f(1)(z)P-1 + f(2)(z)P-2 +...+ f(n)(z)p(n), and an interval P := P-1 x P-2 x...x P-n where p(k) is an element of P-k := [p(k), (p) over bar(k)] subset of R, we construct a real test function T(t) of a real variable t is an element of [a, b] such that (1) holds if (a) there is an f(p) is an element of F such that (1) is true and (b) T(t) > 0 for t is an element of [a, b]. As an application, Kharitonov's theorem [Differentsial'nye Uravneniya 14 No. 11 (1978) 2086-2088] is generalized to real exponential polynomes with some coefficients interval-valued. The problem is treated as one belonging to the theory of functions of one complex variable. (C) 1994 Academic Press, Inc.

[发布日期] 1994-12-01