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Stability Criteria for Systems with Multiple Probabilistic Intervals Time-varying Delay

Zongming Yin, Xiefu Jiang*, Fang Wang
International Journal of Control, Automation, and Systems, vol. 18, no. 4, pp.877-885, 2020

Abstract : The problem of stability for systems with multiple probabilistic intervals time-varying delay is investigated in this paper. First, it is assumed that the probability distributions of the time-varying delay falling into three intervals are known in prior. Two random variables obeying Bernoulli distributions, respectively, are introduced to characterize the probability of the time-varying delay taking values in three intervals. An equivalent new model including the existing ones as its special cases is given. Second, an appropriate Lyapunov-Krasovskii functional is constructed by exploiting more information of delay. Third, based on Lyapunov stability theory, several delay-distribution-dependent stability criteria are derived in the form of linear matrix inequalities by employing Reciprocally convex technique and Generalized Finsler’s lemma. which can provide a larger upper bound of delay compared with the existed ones. Finally, a well-known numerical example is given to show the effectiveness of the proposed method.

Keyword : Linear matrix inequalities(LMIs), Lyapunov-Krasovskii(L-K) functional, probabilistic intervals timevarying delay, stability criteria.

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