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**Output feedback stabilization of linear time-varying uncertain delay systems.**
*(English)*
Zbl 1179.93147

Summary: This paper investigates the output feedback stabilization problem of linear time-varying uncertain delay systems with limited measurable state variables. Each uncertain parameter and each delay under consideration may take arbitrarily large values. In such a situation, the locations of uncertain entries in the system matrices play an important role. It has been shown that if a system has a particular configuration called a triangular configuration, then the system is stabilizable irrespective of the given bounds of uncertain variations. In the results so far obtained, the stabilization problem has been reduced to finding the proper variable transformation such that an \(M\)-matrix stability criterion is satisfied. However, it still has not been shown whether the constructed variable transformation enables the system to satisfy the \(M\)-matrix stability condition. The objective of this paper is to show a method that enables verification of whether the transformed system satisfies the \(M\)-matrix stability condition.

### MSC:

93D15 | Stabilization of systems by feedback |

93B52 | Feedback control |

93C41 | Control/observation systems with incomplete information |

### Keywords:

output feedback stabilization; linear time-varying uncertain delay systems; \(M\)-matrix stability criterion
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\textit{T. Hashimoto} and \textit{T. Amemiya}, Math. Probl. Eng. 2009, Article ID 457468, 14 p. (2009; Zbl 1179.93147)

### References:

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[8] | T. Hashimoto and T. Amemiya, “Controllability and observability invariance of linear time-invariant uncertain systems,” in Proceedings of the International Automatic Control Conference, Tainan, Taiwan, 2008, CD-ROM FA06-4. |

[9] | T. Hashimoto and T. Amemiya, “A note on a criterion for M-matrix,” Computational Mathematics and Modeling, vol. 20, no. 3, pp. 318-325, 2009. · Zbl 1181.15041 |

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