Further Stability Criteria for Sampled-Data-Based Dynamic Positioning Ships Using Takagi–Sugeno Fuzzy Models

Abstract

This article discusses the stability problem of sampled-data-based dynamic positioning ships (DPSs) using Takagi–Sugeno (T-S) fuzzy models. Firstly, dynamic equations for sampled-data DPSs are established. Simultaneously combining several symmetric matrices with new integral terms, a novel Lyapunov–Krasovskii function (LKF) is constructed, which allows the information of a sampling pattern to be fully captured. Next, via the constructed LKF, the positive definiteness requirements of a LKF are further relaxed, and the conservatism of the result can be reduced. Consequently, stability criteria are given, and fuzzy sampled-data controllers are designed in terms of linear matrix inequality (LMI). Finally, a simulation example is provided to verify the superiority and applicability of the developed methods.

Keywords

• fuzzy system
• dynamic positioning ship
• sampled-data control
• Lyapunov–Krasovskii functional
• Takagi−Sugeno fuzzy models