Stability of linear equations with differentiable operators in a hilbert space

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Abstract

We consider the equation $\textrm{d}u(t)/\textrm{d}t=A(t)u(t)$ with an unbounded operator $A(t)$ in a Hilbert space having a bounded strong derivative. We derive the exponential and $L^2$ stability conditions. An illustrative example is presented.

Original languageEnglish
Pages (from-to)19-26
Number of pages8
JournalIMA Journal of Mathematical Control and Information
Volume37
Issue number1
DOIs
StatePublished - 9 Mar 2020

Keywords

  • differential equation in a Hilbert space
  • linear non-autonomous equation
  • stability

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