L2-gain analysis via time-delay approach to periodic averaging with stochastic extension

Jin Zhang*, Emilia Fridman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


We consider perturbed linear systems with fast-varying coefficients that are piecewise-continuous in time. Recently, a constructive time-delay approach to periodic averaging of such systems was introduced that provided an upper bound on the small parameter preserving their input-to-state stability (ISS). In the present paper, we present an improved time-delay approach and extend it to L2-gain analysis. By the backward averaging, we transform the system to a modified time-delay system that leads to fewer terms to be compensated in the Lyapunov–Krasovskii (L–K) analysis. As a result we derive less conservative and simpler conditions for ISS and L2-gain analysis in the form of linear matrix inequalities (LMIs). We further extend our results to stochastic systems where we employ a stochastic extension of Lyapunov functionals that we use for the deterministic case. Two numerical examples (stabilization by vibrational control and by time-dependent switching) illustrate the efficiency of the method.

Original languageEnglish
Article number110126
StatePublished - Mar 2022


FundersFunder number
Israel Science Foundation673/19
Tel Aviv University
Council for Higher Education


    • L-gain analysis
    • LMIs
    • Stochastic systems
    • Time-delay systems


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