A Dynamic Robust Control Approach of Hyperbolic Nonlinear PDE Systems

This paper investigates the exponential stabilization problem for a class of non-affine nonlinear hyperbolic partial differential equation (PDE) systems. A fuzzy modeling approach is employed to express the original system. Then, a fuzzy-model-based dynamic feedback controller is designed to stabilize the PDE system. The sufficient condition on the existence of such a fuzzy controller is developed and presented in terms of spatial differential linear matrix inequalities (SDLMIs) and constructive procedures to obtain the fuzzy controllers are provided. Finally, the effectiveness of the control method is verified by conducting a numerical simulation.