Fuzzy modeling and H∞ control for general 2D nonlinear systems

This paper investigates H∞ control for general 2D nonlinear systems based on a 2D Takagi–Sugeno (T–S) fuzzy model. The system under consideration is an extension of the general 2D linear system to a nonlinear case. Taking the spatial and structural features into consideration, a 2D T–S fuzzy model is first established. In designing the H∞ controller, the inputs are regarded as variables independent from the states and then basis-dependent free matrices are introduced. It has been shown that separation of the input and state variables does not lead to any conservativeness compared with the commonly used method. Thus, a fuzzy H∞ controller is designed using a common free matrix, resulting in only r linear matrix inequalities. The computational advantage is obvious for fuzzy systems with a large number of fuzzy rules. We also demonstrate that the proposed method is less computationally expensive than the approach in which the input variable, state variable and its forward-stepping state are all separately considered, although these two methods can achieve the same optimal H∞ performance. Simulation examples are used to demonstrate the technique and its advantages.