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Trong bài báo này chúng tôi nghiên cứu quang phổ ràng buộc các nhà điều hành thay đổi Mezler theo đa-nhiễu loạn. Characterizations của bán kính ổn định của các nhà khai thác Metzler đối với loại rối loạn được thành lập. Sau đó chúng tôi sẽ áp dụng các kết quả thu được nghiên cứu bán kính ổn định của phương trình chậm trễ trong Lp (-1,0], X). | Vietnam Journal of Mathematics 34 3 2006 357-368 Viet n a m J 0 u r n a I of MATHEMATICS VAST 2006 Robust Stability of Metzler Operator and Delay Equation in Lp -h 0 X B.T. Anh1 N.K. Son2 and D.D.X. Thanh3 1 Department of Mathematics University of Pedagogy 280 An Duong Vuong Str. Ho Chi Minh City Vietnam 2 Institute of Mathematics 18 Hoang Quoc Viet Road 10307 Hanoi Vietnam 3 Department of Mathematics University of Ton Duc Thang 98 Ngo Tat To Str. Ho Chi Minh City Vietnam Received February 16 2006 Abstract. In this paper we study how the spectral bound of Mezler operator changes under multi-perturbations. Characterizations of the stability radius of Metzler operators with respect to this type of disturbances are established. We will then apply the obtained results to study the stability radius of delays equation in Lp -1 0 X . 2000 Mathematics Subject Classification 34K06 93C73 93D09. Keywords Metzler operator stability radius Co-semigroup delay equations. 1. Introduction In the last two decades a considerable attention has been paid to problems of robust stability of dynamic systems in infinite-dimensional spaces. The interested readers are referred to 3 5 6 9 15 and the biography therein for further references. One of the most important problems in the study of robust stability is the calculation of the stability radius of a dynanmic system subjected to various classes of parameter perturbations. In 5 15 explicit formulas for the complex stability radius of a given uniformly exponentially stable linear system x t Ax t under structured perturbations of the form A A DAE 1 358 B. T. Anh N. K. Son and D. D. X. Thanh where A is a closed unbounded operator in a Banach space X D G L U X E G L X Y are given linear bounded operators and A G L Y U is unknown perturbation have been established extending the classical results in finite-dimensional case obtained by Hinrichsen and Pritchard in 8 . The case of time-varying systems has been considered in 9 and 3 where various .
