Observer-Based Fuzzy Control of Uncertain Nonlinear Singular Systems under Multi-Performance Requirements

Abstract

This paper discusses an observer-based fuzzy control problem for uncertain nonlinear singular systems under Multi-Performance Requirements (MPRs). The approach used in the paper is to model the system using a Takagi–Sugeno (T-S) fuzzy model that can be analyzed using linear control theories. The proposed control scheme is based on the Parallel Distributed Compensation (PDC) approach and Proportional Derivative (PD) control scheme. The goal is to design an observer-based fuzzy controller that achieves stability of the system and also satisfies the Guarantee Cost Control (GCC) constraint while maintaining a desired passive constraint. The stability analysis is performed using Lyapunov theory, and the sufficient conditions are transformed into a Linear Matrix Inequality (LMI) form using a Shur Complement, free-weighting matrix method and Singular Value Decomposition (SVD) techniques. The LMI conditions are then solved using convex optimization algorithms. Finally, the proposed control method is validated using a bio-economic system to demonstrate its effectiveness.

Keywords

• T-S fuzzy model
• singular system
• proportional derivative control scheme
• multi-performance fuzzy control
• uncertainty