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

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1 Author(s)
Zhu, J.J. ; Dept. of Electr. & Comput. Eng., Louisiana State Univ., Baton Rouge, LA, USA

Singular behavior of PD-eigenvalues of an nth-order scalar polynomial differential operator (SPDO) 𝒟αnk=1nαk (t)δk-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 𝒟α{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

Published in:

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

Date of Conference:

20-22 Mar 1994