Output Feedback Control of Fuzzy Systems via Reduced-Order Approximation Technique

Abstract

This article focuses on the problem of designing the reduced-order dynamic output feedback (DOF) controller for discrete-time T–S fuzzy plants. Differing from the existing methodologies, the reduced-order approximation technique is applied to simplify the pregiven high-order DOF controller. The key point is to construct a reduced-order closed-loop model to approximate the original high-order closed-loop system. First, a new error auxiliary system between the high-order closed-loop system and the reduced-order closed-loop model is obtained. The sufficient conditions to guarantee that the corresponding error system is asymptotically stable with a prescribed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal{H}_{\infty}$</tex-math> </inline-formula> performance index are developed. Then, the parameters of the desired reduced-order controller are derived by utilizing the projection lemma and the cone complementary linearization algorithm. Finally, the advantages of the proposed technique are illustrated by a series of simulation analysis.