Robust Stability of Linear Evolution Operators on Banach Spaces

This paper introduces a stability radius for a wide class of linear infinite-dimensional time-varying systems under structured time- varying perturbations. A framework is presented that allows the same degree of unboundedness in the perturbations as in the generator of the nominal model.

[1]  田辺 広城,et al.  Equations of evolution , 1979 .

[2]  George Weiss,et al.  Admissibility of unbounded control operators , 1989 .

[3]  Tosio Kato.  Perturbation theory for linear operators , 1966 .

[4]  J. Schwartz,et al.  Linear Operators. Part I: General Theory. , 1960 .

[5]  R. Datko,et al.  Uniform Asymptotic Stability of Evolutionary Processes in a Banach Space , 1972 .

[6]  Tosio Kato,et al.  Integration of the equation of evolution in a Banach space , 1953 .

[7]  Amnon Pazy,et al.  Semigroups of Linear Operators and Applications to Partial Differential Equations , 1992, Applied Mathematical Sciences.

[8]  Jia-An Yan.  A perturbation theorem for semigroups of linear operators , 1988 .

[9]  V. S. Vladimirov.  The Cauchy Problem , 1986 .

[10]  D.L. Elliott,et al.  Feedback systems: Input-output properties , 1976, Proceedings of the IEEE.

[11]  A. J. Pritchard,et al.  The linear quadratic control problem for infinite dimensional systems with unbounded input and outpu , 1987 .

[12]  J. Lions.  Optimal Control of Systems Governed by Partial Differential Equations , 1971 .

[13]  M. Kreĭn,et al.  Stability of Solutions of Differential Equations in Banach Spaces , 1974 .

[14]  Stuart Townley,et al.  A stability radius for infinite dimensional systems , 1987 .

[15]  Stuart Townley,et al.  Robustness of linear systems , 1989 .

[16]  Ruth F. Curtain,et al.  Well-Posedness, stabilizability, and admissibility for Pritchard-Salamon systems , 1992 .

[17]  N. Okazawa.  A Perturbation Theorem for Linear Contraction Semigroups on Reflexive Banach Spaces , 1971 .

[18]  D. Hinrichsen,et al.  Stability radius for structured perturbations and the algebraic Riccati equation , 1986 .