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all-pass antistable Banach space belong to RH Bode plot bound Chapter compute Control coprime coprime factorizations define denoted Desoer dist(fl Edited eigenvalue equals equivalent example Exercise exists factorization G factorization of G feedback system follows formulas H^-norm Hankel operator Hardy space Hence Hilbert space imaginary axis implies inner-outer factorization input Krein Space Lc L0 Lebesgue space left-coprime Lemma linear Lyapunov equations maps matrices in Figure matrix G matrix-valued minimal realization modal subspaces model-matching problem Nehari problem Nehari's theorem nonsingular nonzero norm Nyquist plot operator with symbol optimal Q orthogonal outer poles Pre-multiply proof of Theorem proper and analytic proper real-rational prove Q in RH real-rational functions RHqq Riccati equation right half-plane robust stability satisfying scalar-valued Section signal solution spectral factorization stabilizes G standard problem state-space Step strictly proper Suppose Systems Proceedings theory time-domain transfer function transfer matrix vector X+(A Zames zero