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Abstract— An H∞ control problem with simultaneous consideration of preview and delay is solved, where past signals and future signals are essential to describe behaviors of the control system. Solvability conditions and complete controller parameterization are derived in the frequency domain within the scope of finite dimensional computations, that is,… (More)
It is well known that analytic interpolation theory has found various applications in systems and control, e.g., H∞ control, covariance extension problem for spectral estimation, filtering and gain equalization. For the engineering point of views, it is desirable to synthesize interpolants with bounded degree, where the interpolants correspond to the… (More)
We introduce a coordinate-dependent characteristic of symmetry, which is denoted by C/A. C/A is defined by the division of the covariance (C) by the area (A) of the object of the image. The characteristic has the good properties for the applications to the image processing. We compute the characteristic of ellipse, for which we derive the formula of the… (More)
The existence and uniqueness of the solution to the second-order interpolation problem is proved in terms of topological degree theory.
For a given partial covariance sequence (C<sub>0</sub>, C<sub>1</sub>, ..., C<sub>n</sub>) and for each MA part of the ARMA modeling filter of degree n, an AR part of the ARMA modeling filter of degree n for the solution to the rational covariance extension problem is obtained by solving a nonlinear equation, which is homotopic to a nonlinear equation… (More)
The state-space realization of the multivariable rational interpolant with bounded McMillan degree is given by the block discrete-time Schwarz form. A characterization of the positive realness of the block discrete-time Schwarz form is given by a linear matrix inequality.
In this paper, a property of Schur polynomial of real coe cients and real Toeplitz matrix is given. Suppose that the vector of real coe cients of a Schur polynomial annihilates a real Toeplitz matrix, then the Toeplitz matrix is in fact a zero matrix.