Exponential stability of linear distributed parameter systems with time-varying delays

Emilia Fridman, Yury Orlov

Research output: Contribution to journalArticlepeer-review


Exponential stability analysis via the Lyapunov-Krasovskii method is extended to linear time-delay systems in a Hilbert space. The operator acting on the delayed state is supposed to be bounded. The system delay is admitted to be unknown and time-varying with an a priori given upper bound on the delay. Sufficient delay-dependent conditions for exponential stability are derived in the form of Linear Operator Inequalities (LOIs), where the decision variables are operators in the Hilbert space. Being applied to a heat equation and to a wave equation, these conditions are reduced to standard Linear Matrix Inequalities (LMIs). The proposed method is expected to provide effective tools for stability analysis and control synthesis of distributed parameter systems.

Original languageEnglish
Pages (from-to)194-201
Number of pages8
Issue number1
StatePublished - Jan 2009


  • Distributed parameter systems
  • LMI
  • Lyapunov method
  • Stability
  • Time-varying delay


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