A virtual perturbation method for singular systems
R.L. Klein, Jinhua She, H. Gingold · 1990
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 in 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.>