Title :
A virtual perturbation method for singular systems
Author :
Klein, Ronald L. ; She, Jianming ; Gingold, Harry
Author_Institution :
West Virginia Univ., Morgantown, WV, USA
Abstract :
A virtual perturbation is introduced in a linear time-invariant system Ex(t)=Ax(t)+Bu(t ) with E singular for the purpose of formal regularization. Methods for virtually adding ∈ to get a regular state space system are presented, and a general perturbed form is derived. For the general form a necessary and sufficient convergence condition is derived. A theory of continuous triangularization of matrix functions is presented and applied to obtain an explicit solution of the perturbed system. With such a solution, the system and its asymptotic behavior can be analyzed
Keywords :
convergence; linear systems; matrix algebra; perturbation techniques; asymptotic behavior; continuous triangularization; linear time-invariant system; matrix functions; necessary and sufficient convergence condition; regular state space system; singular systems; virtual perturbation method; Eigenvalues and eigenfunctions; Equations; Frequency domain analysis; Mathematics; Perturbation methods; State-space methods;
Conference_Titel :
Decision and Control, 1990., Proceedings of the 29th IEEE Conference on
Conference_Location :
Honolulu, HI
DOI :
10.1109/CDC.1990.203501
