Delay-dependent methods and the first delay interval

Kun Liu*, Emilia Fridman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


This paper deals with the solution bounds for time-delay systems via delay-dependent Lyapunov-Krasovskii methods. Solution bounds are widely used for systems with input saturation caused by actuator saturation or by the quantizers with saturation. We show that an additional bound for solutions is needed for the first time-interval, where t<τ(t), both in the continuous and in the discrete time. This first time-interval does not influence on the stability and the exponential decay rate analysis. The analysis of the first time-interval is important for nonlinear systems, e.g., for finding the domain of attraction. Regional stabilization of a linear (probably, uncertain) system with unknown and bounded input delay under actuator saturation is revisited, where the saturation avoidance approach is used.

Original languageEnglish
Pages (from-to)57-63
Number of pages7
JournalSystems and Control Letters
Issue number1
StatePublished - Feb 2014


  • First delay interval
  • Input saturation
  • Lyapunov-Krasovskii method
  • Time-varying delay


Dive into the research topics of 'Delay-dependent methods and the first delay interval'. Together they form a unique fingerprint.

Cite this