Parallel D-eigenvalues and parallel D-eigenvectors for linear time-varying systems

Author

Zhu, J. Jim

Author_Institution

Dept. of Electr. & Comput. Eng., Louisiana State Univ., Baton Rouge, LA, USA

fYear

1994

fDate

20-22 Mar 1994

Firstpage

297

Lastpage

301

Abstract

Singular behavior of PD-eigenvalues of an nth-order scalar polynomial differential operator (SPDO) 𝒟_α=δ ⁿ+Σ_k=1ⁿα_k(t)δ^k-1, where δ=d/dt, is investigated. Main results of this paper include: (i) definition and properties of PD-eigenvectors associated with PD-eigenvalues, (ii) definitions and properties of generalized PD-eigenvectors and generalized PD-eigenvalues for singular PD-eigenvalues; (iii) application of (i) and (ii) in stability analysis of linear time-varying (LTV) systems 𝒟_α{y}=0, and (iv) application (i) and (ii) in the realization of PD-characteristic equation. The new results will have a significant impact on applications of the unified eigenvalue theory to the analysis and control of LTV control systems, and its further development

Keywords

eigenvalues and eigenfunctions; linear systems; matrix algebra; polynomials; stability; time-varying systems; PD characteristic equation; linear time varying systems; nth-order scalar polynomial differential operator; parallel D-eigenvalues; parallel D-eigenvectors; stability; Control system analysis; Control systems; Eigenvalues and eigenfunctions; Image processing; Laboratories; Polynomials; Remote sensing; Riccati equations; Stability analysis; Time varying systems;

fLanguage

English

Publisher

ieee

Conference_Titel

System Theory, 1994., Proceedings of the 26th Southeastern Symposium on

Conference_Location

Athens, OH

ISSN

0094-2898

Print_ISBN

0-8186-5320-5

Type

conf

DOI

10.1109/SSST.1994.287865

Filename

287865