Stability property and essential spectrum of linear retarded functional differential equations

  • Authors:

  • Kai Liu;Liangjian Hu;Jiaowan Luo

  • Affiliations:

  • School of Information and Mathematics, Yangtze University, Jingzhou, Hubei, 434023, PR China and Department of Mathematical Sciences, The University of Liverpool, Liverpool, L69 7ZL, UK;Department of Applied Mathematics, Donghua University, Shanghai, 201620, PR China;School of Mathematics and Information Sciences, Guangzhou University, Guangzhou, Guangdong, 510006, PR China

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2013

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Abstract

In this work, we shall study stability and stabilization of a class of retarded functional differential equations in Banach spaces. We present sufficient (and necessary, sometimes) conditions for weak, asymptotic and exponential stability properties. It is shown that retarded growth bounds are totally determined by retarded non-isolated spectra, isolated eigenvalues with infinite algebraic multiplicity and spectral bounds. Stabilization problem via compact perturbations, a topic which is practically useful in the context of control theory of dynamical systems, is considered as well.