Title: Design of robust H_∞ fuzzy output feedback controller for affine nonlinear systems: fuzzy Lyapunov function approach

Authors: Leila Rajabpour; Mokhtar Shasadeghi; Alireza Barzegar

Addresses: Department of Electronic Engineering, University of Technology Malaysia, Malaysia ' Department of Electronic Engineering, Shiraz University of Technology, Shiraz, Iran ' Department of Electronic Engineering, Nanyang Technological University, Singapore

Abstract: In this paper, we propose a new systematic approach based on non-quadratic 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_∞ controller is designed based on parallel distributed compensation (PDC) scheme. Then, the stability conditions are derived in terms of linear matrix inequalities (LMIs) by utilising 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.

Keywords: T-S fuzzy bilinear model; robust H_∞ controller; fuzzy output feedback controller; fuzzy Lyapunov function; linear matrix inequality; slack matrices; CSTR benchmark.

DOI: 10.1504/IJAIP.2019.103441

International Journal of Advanced Intelligence Paradigms, 2019 Vol.14 No.3/4, pp.328 - 344

Received: 22 Feb 2017
Accepted: 02 Mar 2018
Published online: 06 Nov 2019 *

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