Sampled-data implementation of extended PID control using delays

Jin Zhang*, Emilia Fridman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


We study the sampled-data implementation of extended PID control using delays for the nth-order stochastic nonlinear systems. The derivatives are approximated by finite differences giving rise to a delayed sampled-data controller. An appropriate Lyapunov–Krasovskii (L-K) method is presented to derive linear matrix inequalities (LMIs) for the exponential stability of the resulting closed-loop system. We show that with appropriately chosen gains, the LMIs are always feasible for small enough sampling period and stochastic perturbation. We further employ an event-triggering condition that allows to reduce the number of sampled control signals used for stabilization and provide (Formula presented.) -gain analysis. Finally, three numerical examples illustrate the efficiency of the presented approach.

Original languageEnglish
Pages (from-to)9610-9624
Number of pages15
JournalInternational Journal of Robust and Nonlinear Control
Issue number18
StatePublished - Dec 2022


FundersFunder number
Council for Higher Education, Israel Funding information
Ministry of Education and Science of the Russian Federation075‐15‐2021‐573
Israel Science Foundation673/19
Council for Higher Education


    • -gain analysis
    • PID control
    • event-triggered control
    • sampled-data control
    • stochastic perturbations


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