Abstract
This paper is concerned with perturbation problems of regularity linear systems. Two types of perturbation results are proved: (i) the perturbed system (A + P, B, C) generates a regular linear system provided both (A, B, C) and (A, B, P) generate regular linear systems; and (ii) the perturbed system \({((A_{-1}+\Delta A)|_X,B,C^A_\Lambda)}\) generates a regular linear system if both (A, B, C) and (A, ΔA, C) generate regular linear systems. These allow us to establish a new variation of constants formula of the control system (A + P, B). Moreover, these results are applied to the linear systems with state and output delays. The regularity and the mild expressibility is deduced, and a necessary and sufficient condition for stabilizability of the delayed systems is proved.
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