Frequency-domain estimates of the sampling interval in multirate nonlinear systems by time-delay approach

T. A. Bryntseva, A. L. Fradkov

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4 Scopus citations


A class of nonlinear hybrid systems consisting of a continuous plant and a multirate sampled-data controller is considered. Applying the time-delay approach, the system is transformed to the system with a time-varying sawtooth delay. Then, the value of the sampling intervals ensuring stability of the closed-loop system is estimated based on the frequency-domain circle-like criterion for systems with time-varying delay. Such a criterion for multirate MIMO systems is established based on the previous result for SISO systems proposed by M.Churilova in 1995. Efficiency and advantages of the method are illustrated by numerical examples. The key advantage of the proposed approach is that it is applicable to multirate systems nonaffine in control. It allows one to use a nonlinear feedback for stabilisation. Particularly, the case of nonsmooth or discontinuous nonlinear systems can be treated.

Original languageEnglish
Pages (from-to)1985-1992
Number of pages8
JournalInternational Journal of Control
Issue number9
StatePublished - 2 Sep 2019

Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications


  • frequency domains
  • hybrid systems
  • Lyapunov function
  • multirate systems
  • sampling intervals
  • Stability of nonlinear systems


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