Delay-range-dependent stabilization of uncertain dynamic systems with interval time-varying delays.

*(English)*Zbl 1170.34054
Appl. Math. Comput. 208, No. 1, 58-68 (2009); erratum ibid. 215, No. 1, 427-430 (2009).

Linear continuous-time control systems with variable coefficients and variable point delay in the state variables are considered. It is generally assumed that the system matrices are known with some uncertainties. Using Lyapunov functionals and linear matrix inequality, sufficient conditions for feedback stabilizability are formulated and proved. Simple numerical examples, which illustrate theoretical considerations are presented. Moreover, many remarks and comments on stabilization problems for delayed control systems are given. The relationships to the results existing in the literature are mentioned and discussed. Finally, it should be pointed out, that similar stabilization problems have been recently considered in the papers [J. H. Park and O. Kwon, Appl. Math. Comput. 162, No. 2, 627–637 (2005; Zbl 1077.34075)] and [P. G. Park and J. W. Ko, Stability and robust stability for systems with a time-varying delay. Automatica 43, No. 10, 1855–1858 (2007; Zbl 1120.93043)].

Reviewer: Jerzy Klamka (Gliwice)

##### MSC:

34K35 | Control problems for functional-differential equations |

93C05 | Linear systems in control theory |

93C23 | Control/observation systems governed by functional-differential equations |

93D09 | Robust stability |

93D15 | Stabilization of systems by feedback |

34K06 | Linear functional-differential equations |

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\textit{O. M. Kwon} and \textit{J. H. Park}, Appl. Math. Comput. 208, No. 1, 58--68 (2009; Zbl 1170.34054)

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