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On the Perturbations of Regular Linear Systems and Linear Systems with State and Output Delays

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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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Authors and Affiliations

  1. Department of Mathematics, Xi’an Jiaotong University, Xi’an, 710049, China

    Zhan-Dong Mei & Ji-Gen Peng

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  1. Zhan-Dong Mei
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  2. Ji-Gen Peng
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Correspondence to Zhan-Dong Mei.

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This work was supported by the NSFC under the contact 60970149.

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Mei, ZD., Peng, JG. On the Perturbations of Regular Linear Systems and Linear Systems with State and Output Delays. Integr. Equ. Oper. Theory 68, 357–381 (2010). https://doi.org/10.1007/s00020-010-1793-8

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  • DOI: https://doi.org/10.1007/s00020-010-1793-8

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