Stability of singularly perturbed differential-difference systems: A LMI approach

E. Fridman*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


For linear singularly perturbed system with delay sufficient conditions for stability for all small enough values of singular perturbation parameter ε are obtained in the general case, when delay and ε are independent. The sufficient delay-dependent conditions are given in terms of linear matrix inequalities (LMIs) by applying an appropriate Lyapunov-Krasovskii functional. LMIs are derived by using a descriptor model transformation and Park's inequality for bounding cross terms. A memoryless state-feedback stabilizing controller is obtained. Solution is given also in the case of systems with polytopic parameter uncertainties. Numerical examples illustrate the effectiveness of the new theory.

Original languageEnglish
Pages (from-to)201-212
Number of pages12
JournalDynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms
Issue number2
StatePublished - Jun 2002


  • Delay-dependent criteria
  • LMI
  • Singular perturbations
  • Stability
  • Time-delay systems


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