Discrete-time robust fuzzy control synthesis for discretized and perturbed ship fin stabilizing systems subject to variance and pole location constraints

Abstract

A discrete-time robust fuzzy controller design problem for the discretized and perturbed nonlinear ship fin stabilizing systems is studied in this paper. The discrete-time Takagi–Sugeno fuzzy model is used to represent the nonlinear ship fin stabilizing systems. The control performance considered in this paper includes stability requirement, pole location constraint, individual state variance constraint, and minimum output variance. Applying the Lyapunov theory, a discrete-time robust fuzzy controller is designed based on parallel distributed compensation technology and the relevant conditions are deduced in the form of linear matrix inequalities. By solving these conditions, a discrete-time robust fuzzy controller can be obtained to satisfy the above performance constraints. At last, a simulation for controlling a discrete-time nonlinear ship fin stabilizing system is provided to show the feasibility and applicability of the proposed robust fuzzy control method.