Stability analysis for linear delayed systems via an optimally dividing delay interval approach.

*(English)*Zbl 1227.93092
Automatica 47, No. 9, 2126-2129 (2011); corrigendum ibid. 50, No. 6, 1739-1740 (2014).

Summary: This paper addresses the problem of stability for linear systems with time-varying delay. A novel augmented Lyapunov-Krasovskii functional is constructed by using the idea of optimally dividing the delay interval \([0,\tau (t)]\) into some variable sub-intervals and using the line integral technology. Using the novel augmented functional, a new delay-dependent stability criterion is proposed for linear systems with time-varying delay. The gain is that this stability criterion can lead to much less conservative stability results compared to other methods for linear systems with delay. Two numerical examples are provided to verify the effectiveness of the proposed criteria.

##### MSC:

93D09 | Robust stability |

93C05 | Linear systems in control theory |

93C15 | Control/observation systems governed by ordinary differential equations |

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\textit{H. Zhang} and \textit{Z. Liu}, Automatica 47, No. 9, 2126--2129 (2011; Zbl 1227.93092)

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##### References:

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