Passive Stabilization of Static Output Feedback of Disturbed Nonlinear Stochastic System

Abstract

This paper investigates the Static Output (SO) control issue of the disturbed nonlinear stochastic system, which achieves passivity. Through the application of fuzzy sets and the stochastic differential equation, a Takagi–Sugeno (T-S) fuzzy model with the terms of multiplicative noise and external disturbance can be constructed to describe the considered systems. Furthermore, the Parallel Distributed Compensation (PDC) concept is used to design a fuzzy controller exhibiting an SO feedback scheme structure. To attenuate the effect of external disturbance, the PDC-based SO fuzzy controller is designed to exhibit passivity. During the derivation of some sufficient conditions, a line-integral Lyapunov function is utilized to avoid the conservative term produced using the derivative membership function. Using converting technologies, a stability criterion belonging to Linear Matrix Inequality (LMI) forms is proposed such that the derived conditions are convex hull problems and are solved through an optimization algorithm. Then, the proposed criterion is used to discuss the problem of SO controller design of ship fin stabilizing systems with added disturbance and noise.