Delayed non-fragile H<inf>∞</inf> control for offshore steel jacket platforms

This paper is concerned with non-fragile H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> control for offshore steel jacket platforms subject to self-excited nonlinear wave force and external disturbances. A delayed non-fragile H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> controller is designed to attenuate the oscillation amplitudes of the offshore platform. The positive effects of the time-delays on non-fragile H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> control for the offshore platform are investigated. It is shown through simulation results that (i) the proposed non-fragile H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> controller is effective to reduce the vibration of the offshore platform; (ii) the control force required by the delayed non-fragile H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> controller is smaller than the one by the delay-free non-fragile H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> controller; and (iii) the allowable maximum time-delay under the delayed non-fragile H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> controller is much larger than the one under the delayed dynamic output feedback controller.