Interpolation theory and λ-matrices

K Hariche, E.D Denman
1989 Journal of Mathematical Analysis and Applications  
This paper shows how interpolation theory can be used in the structural analysis of I-matrices, which often occur in the description of the dynamics of multivariable systems. Using scalar interpolatory polynomials for the linear I-matrix case and interpolatory I-matrices for the general case, a set of spectral projectors is derived. The fundamental properties of the interpolatory polynomials and I-matrices are derived and used to develop a suitable form for the resolvent. 0 1989 Academic Press,
more » ... Inc. The theory of A-matrices is becoming important in the study of large space structures as well as in other areas of control theory. The lack of a complete theory for A-matrices, at least to the extent that the theory for first order state variable systems exists, has hindered development of algorithms for A-matrices. This is especially true for large space structures where identification and control will be important in placing large flexible structures on orbit. Since flexible structures are generally characterized by second order A-matrices, it is important that the theory of A-matrices be developed to the maximum extent that is possible. The earlier work of Lancaster [l] plays an important role in most of the current literature on the subject matter. The later work of Dennis, Traub and Webber [2] deserves an important place in the literature on A-matrices. The most recent work of Lancaster, with Tismentsky [3], should be mentioned as this book covers material not included in the earlier work of Lancaster. The work of Gantmacher [4] should be noted as the two volumes on matrices are perhaps the outstanding works on matrix theory in the open literature today. Recent work on solvents and projectors by one of the authors and other
doi:10.1016/0022-247x(89)90058-9 fatcat:ofusnajq35crbeuii3b2xqfhdy