Controller synthesis for positive Takagi-Sugeno fuzzy systems under ℓ₁ performance

ABSTRACT

In this paper, the problem of ℓ₁-induced controller design for positive Takagi-Sugeno (T-S) fuzzy systems is investigated with the use of linear Lyapunov function. A novel performance characterisation is first established to guarantee the asymptotic stability of the closed-loop system with ℓ₁-induced performance. Moreover, sufficient conditions are presented to design the required fuzzy controllers and iterative convex optimisation approaches are developed to solve the conditions. Finally, two examples are presented to show the effectiveness of the derived theoretical results.

KEYWORDS:

• Iterative algorithm
• linear Lyapunov functions
• ℓ₁-induced performance
• positive T-S fuzzy systems

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is partially supported by General Research Fund, University of Hong Kong [grant number 17204014] and National Natural Science Foundation of China [grant number 61503184, 61174102].