Wirtinger's inequality and Lyapunov-based sampled-data stabilization

Kun Liu*, Emilia Fridman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Discontinuous Lyapunov functionals appeared to be very efficient for sampled-data systems (Fridman, 2010; Naghshtabrizi, Hespanha, & Teel, 2008). In the present paper, new discontinuous Lyapunov functionals are introduced for sampled-data control in the presence of a constant input delay. The construction of these functionals is based on the vector extension of Wirtinger's inequality. These functionals lead to simplified and efficient stability conditions in terms of Linear Matrix Inequalities (LMIs). The new stability analysis is applied to sampled-data state-feedback stabilization and to a novel sampled-data static output-feedback problem, where the delayed measurements are used for stabilization.

Original languageEnglish
Pages (from-to)102-108
Number of pages7
Issue number1
StatePublished - Jan 2012


  • LMI
  • LyapunovKrasovskii functional
  • Sampled-data systems
  • Time-delay


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