State variance constrained fuzzy controller design for nonlinear TORA systems with minimizing control input energy

This paper presents a model-based fuzzy control of translational oscillations with a proof mass actuator (TORA), which is well known as a nonlinear control benchmark problem. In this paper, the nonlinear TORA system is modeled by the Takagi-Sugeno (T-S) fuzzy stochastic system. For this TS type fuzzy model, we design the T-S fuzzy controller which not only ensure the stability of the closed-loop system, but also minimize the control input energy with state variance constraints. The present method uses Linear Matrix Inequalities (LMI) approach to find the common positive definite covariance matrix and feedback gains for each rule of the TORA TS fuzzy stochastic systems.