Dissipative Control for Single Flexible Joint Robotic System via T–S Fuzzy Modelling Approach

Abstract

The dissipativity analysis for single flexible joint robotic system via Takagi–Sugeno (T–S) fuzzy modelling technique is the main focus of this paper. Our aim is to design a delayed state feedback controller by using parallel distributed compensation (PDC) so that the considered system is asymptotically stable with a (Φ1, Φ2, Φ3)-γ- dissipative performance index. A delay-range-dependent strictly (Φ1, Φ2, Φ3) -γ- dissipativity condition is derived in terms of linear matrix inequality (LMI) framework by constructing an appropriate Lyapunov– Krasovskii functional (LKF) and using higher order polynomial based integral inequality (HOPBII) to estimate its derivative. Finally, numerical simulation result is given to show the effectiveness of the proposed theoretical method.