loading page

Relaxed Static Output Stabilization of Polynomial Fuzzy Control Systems by Lagrange Membership Functions
  • +2
  • Xiaomiao Li,
  • Zhiyong Bao,
  • Sike Li,
  • Yuehao Du,
  • Fucai Liu
Xiaomiao Li
Yanshan University School of Electrical Engineering

Corresponding Author:[email protected]

Author Profile
Zhiyong Bao
Yanshan University School of Electrical Engineering
Author Profile
Sike Li
Yanshan University School of Electrical Engineering
Author Profile
Yuehao Du
Yanshan University School of Electrical Engineering
Author Profile
Fucai Liu
Yanshan University School of Electrical Engineering
Author Profile

Abstract

This paper is concerned with the stability analysis of the static output-feedback polynomial fuzzy-model-based (SOF PFMB) control systems through designing a novel membership grade integration (MGI) approach. The nonconvex problems of the SOF PFMB control systems are convexificated into the convex conditions by introducing block diagonal positive-definite Lyapunov matrix and nonsingular transformation matrix. We proposed a new approximated membership functions, i.e. Lagrange Membership Functions (LMFs) method, which can be introduced into the stabilization process to relieve the stability conservativeness results. The LMFs are general representations of piecewise-linear membership functions (PLMFs), which makes the number of stability conditions not limited by the number of sample points. In a fixed subdomain, arbitrary sample points can be employed by the LMFs method and achieve higher approximation capability by increasing more sample points, so that membership grades can be incorporated into the system analysis. Furthermore, a novel MGI approach including the information of premise variables and LMFs are proposed, which can make the stability conditions more relaxed. Finally, a simulation example is given to show the merits of the developed techniques.
03 Nov 2023Submitted to International Journal of Robust and Nonlinear Control
03 Nov 2023Assigned to Editor
03 Nov 2023Submission Checks Completed
03 Nov 2023Review(s) Completed, Editorial Evaluation Pending
15 Nov 2023Reviewer(s) Assigned