Robust and reliable H<inf>∞</inf> fuzzy hyperbolic decentralized control for a class of nonlinear large-scale systems with parametric uncertainties

Abstract

This paper develops robust H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> fuzzy hyperbolic control for nonlinear large-scale systems with parameter uncertainties. Firstly, fuzzy hyperbolic model (FHM) can be used to establish the model for certain complex large-scale systems, then according to the Lyapunov direct method and the decentralized control theory of large-scale systems, the sufficient condition in the terms of linear matrix inequalities (LMIs) which guarantee the existence of the state feedback H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> control based on FHM for the fuzzy large-scale systems is proposed. The main advantage of using FHM over Takagi-Sugeno (T-S) fuzzy model is that no premise structure identification is needed and no completeness design of premise variables space is needed, therefore there needs much less computation expense than that of using T-S fuzzy model, especially when a lot of fuzzy rules are needed to approximate highly nonlinear complex systems. In addition, an FHM is not only a kind of valid global description but also a kind of nonlinear model in nature. A simulation example is provided to illustrate the design procedure of the proposed method and its validity.