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

摘要

Singular behavior of PD-eigenvalues of an nth-order scalar polynomial differential operator (SPDO) /spl Dscrsub /spl alpha=/spl deltasup n/+/spl Sigmasub k=1sup nspl alphasub k/(t)/spl deltasup k/spl minus/1/, where /spl delta/=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 /spl Dscrsub /spl alpha/spl lcub/y/spl rcub/=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.