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**On robust stability criterion for dynamic systems with time-varying delays and nonlinear perturbations.**
*(English)*
Zbl 1168.34354

Appl. Math. Comput. 203, No. 2, 937-942 (2008); erratum ibid. 215, No. 1, 427-430 (2009).

Authors’ abstract: We propose a new delay-dependent stability criterion for dynamic systems with time-varying delays and nonlinear perturbations. Based on the Lyapunov method, a sufficient delay-dependent criterion for asymptotic stability is derived in terms of linear matrix inequality. Numerical examples are given to show the effectiveness of our result.

Reviewer’s comment: On the first glance the setting of the problem is different from that one in the paper of the same authors, published in the same journal and volume [Appl. Math. Comput. 203, No. 2, 843–853 (2008; Zbl 1168.34046)]. Here, the problem is nonlinear, whereas it is linear in the cited paper. However, if one considers the nonlinearities as the uncertainty terms in the cited paper, both settings become less or more the same. So, nothing to wonder that also the approaches and the results are similar. So, one wonders after all, why no one of the two papers contains a reference to the other one.

Reviewer’s comment: On the first glance the setting of the problem is different from that one in the paper of the same authors, published in the same journal and volume [Appl. Math. Comput. 203, No. 2, 843–853 (2008; Zbl 1168.34046)]. Here, the problem is nonlinear, whereas it is linear in the cited paper. However, if one considers the nonlinearities as the uncertainty terms in the cited paper, both settings become less or more the same. So, nothing to wonder that also the approaches and the results are similar. So, one wonders after all, why no one of the two papers contains a reference to the other one.

Reviewer: Ivan Ginchev (Varese)

### MSC:

34K20 | Stability theory of functional-differential equations |

34K40 | Neutral functional-differential equations |

93D09 | Robust stability |

### Keywords:

robust stability; neutral systems; Lyapunov method; linear matrix inequality; interval time-vatying delay.### Citations:

Zbl 1168.34046### Software:

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\textit{O. M. Kwon} et al., Appl. Math. Comput. 203, No. 2, 937--942 (2008; Zbl 1168.34354)

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### References:

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