Observer-Based Fuzzy l2-l∞ Control for Discrete-Time Nonlinear Systems

• Published in: IEEE transactions on fuzzy systems Vol. 32; no. 4; pp. 2523 - 2528
• Main Authors: Chang, Xiao-Heng, Han, Xu
• Format: Journal Article
• Language: English
• Published: IEEE 01.04.2024
• Subjects: <named-content xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" content-type="math" xlink:type="simple"> <inline-formula> <tex-math notation="LaTeX"> l_{2}</tex-math> </inline-formula> </named-content>–<named-content xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" content-type="math" xlink:type="simple"> <inline-formula> <tex-math notation="LaTeX"> l_\infty</tex-math> </inline-formula> </named-content> control; Closed loop systems; Discrete-time nonlinear systems; Fuzzy systems; Linear matrix inequalities; linear matrix inequality (LMI); Lyapunov methods; observer; Observers; Performance analysis; Stability criteria; Takagi-Sugeno model; Takagi–Sugeno (T–S) fuzzy model
• ISSN: 1063-6706
• DOI: 10.1109/TFUZZ.2023.3348231

In this article, an observer-based <inline-formula><tex-math notation="LaTeX">l_{2}</tex-math></inline-formula>-<inline-formula><tex-math notation="LaTeX">l_\infty</tex-math></inline-formula> performance analysis and controller design problem is proposed for a category of discrete-time nonlinear control systems. First of all, the closed-loop system with external disturbance in both state and output variables under consideration is represented as a discrete-time Takagi-Sugeno (T-S) fuzzy model and is described by the descriptor representation method. Subsequently, a new Lyapunov function is suggested that satisfies the prescribed <inline-formula><tex-math notation="LaTeX">l_{2}</tex-math></inline-formula>-<inline-formula><tex-math notation="LaTeX">l_\infty</tex-math></inline-formula> performance while ensuring stability. The application of the linear matrix inequality technique is employed to establish an analysis criterion for the <inline-formula><tex-math notation="LaTeX">l_{2}</tex-math></inline-formula>-<inline-formula><tex-math notation="LaTeX">l_\infty</tex-math></inline-formula> performance. By defining the structure of matrix variables, new design conditions of observer-based <inline-formula><tex-math notation="LaTeX">l_{2}</tex-math></inline-formula>-<inline-formula><tex-math notation="LaTeX">l_\infty</tex-math></inline-formula> controller are given. Ultimately, an instance demonstrates the effectiveness of the proposed controller design criterion.