Robust mixed H∞ /passive vibration control of offshore steel jacket platforms with structured uncertainty

Abstract This paper focuses on the problems associated with designing a robust mixed H ∞ /passive controller for offshore steel jacket platforms with structured uncertainty. The objective of this paper is to design a controller that is meant to stabilize the offshore platform dynamic when exposed to structured uncertainties. This designation must also satisfy a mixed H ∞ /passive performance index. In order to design such a controller, at first, the instantaneous state feedback controller ought to be considered. Then, mixed time-delayed states and instantaneous states are to be considered in such a way that the control law covers various kinds of practical situations. Based on the Lyapunov-Krasovskii Functional (LKF), some stability criteria are obtained and expressed in the form of Linear Matrix Inequalities (LMIs). According to these stability criteria, some sufficient conditions for the existence of the state feedback controller gain are to be met. At the end, the designed controllers are applied to the model of the offshore platform with uncertainty before numerically simulating the effectiveness of the proposed methods.

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