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Stability Criteria for Systems with Multiple Probabilistic Intervals Time-varying Delay
Zongming Yin,Xiefu Jiang,Fang Wang 제어·로봇·시스템학회 2020 International Journal of Control, Automation, and Vol.18 No.4
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.
Vibration Reduction for Offshore Platforms via Delayed Sliding Mode H∞ Control
Bao-Lin Zhang,Xiefu Jiang,Qiuxuan Wu,Gong-You Tang 제어·로봇·시스템학회 2019 International Journal of Control, Automation, and Vol.17 No.1
This paper deals with delayed sliding mode H∞ control for an offshore steel jacket platform subject tononlinear self-excited wave force and external disturbance. By using both current and delayed states, a delayedsliding mode H∞ controller is designed to attenuate vibration of the offshore platform. It is observed throughsimulation results that the delayed sliding mode H∞ controller is capable of reducing the oscillation amplitudesof the offshore platform significantly. Moreover, compared with the delay-free sliding mode H∞ controller, theoscillation amplitudes of the offshore platform under the controllers are almost the same, while the control forcerequired by the delayed sliding mode H∞ controller is less than that by the delay-free sliding mode H∞ controller.