Design of robust H_inf fuzzy output feedback controller for affine nonlinear systems:Fuzzy Lyapunov function approach

TL;DR

This paper introduces a systematic method for designing robust H_inf fuzzy output feedback controllers for affine nonlinear systems using Lyapunov functions and slack matrices, demonstrated on a chemical reactor model.

Contribution

It presents a novel approach combining nonquadratic Lyapunov functions and slack matrices to reduce conservativeness in H_inf fuzzy control design for affine nonlinear systems.

Findings

Reduced conservativeness in stability conditions via slack matrices

Effective control design demonstrated on a chemical reactor model

Lyapunov-based LMI conditions ensure robust stability and performance

Abstract

In this paper, we propose a new systematic approach based on nonquadratic Lyapunov function and technique of introducing slack matrices, for a class of affine nonlinear systems with disturbance. To achieve the goal, first, the affine nonlinear system is represented via Takagi-Sugeno (T-S) fuzzy bilinear model. Subsequently, the robust H_inf controller is designed based on parallel distributed compensation (PDC) scheme. Then, the stability conditions are derived in terms of linear matrix inequalities (LMIs) by utilizing Lyapunov function. Moreover, some slack matrices are proposed to reduce the conservativeness of the LMI stability conditions. Finally, for illustrating the merits and verifying the effectiveness of the proposed approach, the application of an isothermal continuous stirred tank reactor (CSTR) for Van de Vusse reactor is discussed in details.