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A State‐Space Based New Approach To The Directional Interpolation Problem
Author(s) -
Horiguchi Kazumi
Publication year - 2002
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1111/j.1934-6093.2002.tb00356.x
Subject(s) - interpolation (computer graphics) , mathematics , transformation (genetics) , bounded function , realization (probability) , linear interpolation , linear fractional transformation , computation , mathematical optimization , inverse quadratic interpolation , state space , function (biology) , trilinear interpolation , transformation matrix , bilinear interpolation , spline interpolation , algorithm , computer science , mathematical analysis , control system , robust control , artificial intelligence , motion (physics) , chemistry , polynomial , biology , biochemistry , kinematics , classical mechanics , evolutionary biology , statistics , physics , gene , engineering , electrical engineering
Directional interpolation plays an important role in robust control, system realization and model reduction. Several solutions to various directional interpolation problems have been proposed. In this paper, we consider the directional interpolation problem in a general setting and present a statespace based new approach to solving the problem. The solution is simple, and its exposition is as self‐contained as possible. We describe all the (strictly) bounded real rational matrix functions that satisfy the directional interpolation requirements by means of linear fractional transformation. Moreover, we give a necessary and sufficient condition for the interpolating function to be unique and show that the unique interpolating function is an inner (a co‐inner). The main procedures used to generate the interpolating function consist of standard matrix operations consisting of easy numerical computations, so the present solution is significant from the numerical viewpoint as well as the analytical viewpoint.