화학공학소재연구정보센터
IEEE Transactions on Automatic Control, Vol.39, No.6, 1262-1263, 1994
A Counterexample on Continuous Coprime Factors
In [1], the following question was raised : Consider a linear, shift-invariant system on L2[0, infinity). Let the graph of the system have Fourier transform (M/N) H-2 (i.e., the system has a transfer function P = N/M) where M, N are elements of C(A) = {f is-an-element-of H(infinity) : f is continuous on the compactified right-half plane}. Is it possible to normalize M and N (i.e., to ensure M2 + N2 = 1) in C(A)? Here, we show by example that this is not always possible.