Controller Design for a Class of Nonlinear Systems Based on Fuzzy Hyperbolic Model

Abstract

In this paper, a fuzzy hyperbolic H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> controller (FHC), for a class of nonlinear systems based on fuzzy hyperbolic model (FHM), is proposed. FHM is a universal approximator, and can be used to establish the model for unknown complex systems. Moreover, the main advantage of using FHM over T-S fuzzy model is that no premise structure identification is need and no completeness design of premise variables space is need. Also an FHM is a kind of valid global description and nonlinear model inherently. Firstly, an FHM is proposed to represent the state-space model for nonlinear systems. Secondly, considering the influence of both approximation error and external disturbance, fuzzy hyperbolic H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> control scheme is addressed by solving a set of linear matrix inequalities (LMIs). Some free-weighting matrices are introduced to express the relationships among the system variables. The results are then easily extended to a system with polytopic-type uncertainties. Simulation research shows the validity of this control scheme.