Synthesis of Fuzzy Control for Inverter Pendulum Robot with H ∞ Performance Constraint

Abstract

Abstract—The purpose of this paper is to give one set of stability and stabilization conditions for an inverted pendulum robot which simulating human stance under the framework of Discrete Perturbed Time-Delay Affine (DPTDA) Takagi– Sugeno (T–S) fuzzy models. In the beginning, the mathematical model of inverted pendulum robot system and the corresponding DPTDA T–S fuzzy model are introduced. Next, some sufficient conditions are derived on robust H disturbance attenuation, in which the robust stability and prescribed performance are achieved. In order to find suitable fuzzy controllers, the Iterative Linear Matrix Inequality (ILMI) algorithm is employed to solve these sufficient conditions. Finally, a numerical simulation for the nonlinear inverted pendulum robot system is given to show the applications of the presented controller design approach.