Guaranteed cost fuzzy state observer design for semilinear parabolic PDE systems under pointwise measurements

Abstract

This paper studies the guaranteed cost fuzzy state observer (GCFSO) design via pointwise measurement sensors for a class of distributed parameter systems described by semilinear parabolic partial differential equations (PDEs). Initially, a Takagi–Sugeno (T–S) fuzzy model is employed to accurately represent the original PDE system in a local region. Then, based on the T–S fuzzy model, a fuzzy state observer is constructed for the state estimation. By augmenting the state estimation error system with the fuzzy PDE system and utilizing Lyapunov technique and Wirtinger’s inequality, a fuzzy state observer design with a guaranteed cost is developed in terms of linear matrix inequalities (LMIs). The resulting fuzzy observer can exponentially stabilize the augmented system while providing an upper bound on the cost function of state estimation error. Moreover, a suboptimal GCFSO design problem is also addressed to make the upper bound as small as possible. Finally, the numerical simulation results on two examples demonstrate the effectiveness of the proposed method.