A Parameterization of Positive Real Residue Interpolants with McMillan Degree Constraint

Abstract: The main body of this thesis consists of six appended papers.The papers are about the theory of the positive real interpolationwith McMillan degree constraint.In Paper A, a parameterization of the positive real residue interpolantswith McMillan degree constraint is given.For a given interpolation data and for each free parameter,a positive real interpolant, of which McMillan degree isequal to the McMillan degree of the maximum entropy interpolant, is obtained bysolving a nonlinear equation, which is homotopic to a nonlinear equation to determinethe maximum entropy interpolant.In Paper B,the state-space realization of the multivariable rational interpolant with bounded McMillan degreeis given by the block discrete-time Schwarz form.A characterization of the positive realness of the block discrete-time Schwarz form isgiven by a linear matrix inequality.In Paper C,a robust controller synthesis for the mismatch of delay in terms ofthe Nevanlinna-Pick interpolation is presented.In Paper D,a Smith predictor synthesis for unstable and minimum-phaseinput delay system and for a first orderunstable distributed delay system is given in terms of the Nevanlinna-Pick interpolation.In Paper E , we study an approximation of spectral density in termsof the generalized Kullback-Leibler distance minimization.For a given spectral density,we seek a spectraldensity by minimizingthe generalized Kullback-Leibler distance subject to a constraint onthe tangential second-orderstatistics.In Paper F, a property of Schur polynomial of real coefficientsand real Toeplitz matrix is given.Suppose that the vector of coefficients of a Schur polynomial annihilatesa Toeplitz matrix, then the Toeplitz matrix is in facta zero matrix.