Abstract
In this paper, an optimal controller design for a system with time varying and non-smooth non-linearities described by Takagi-Sugeno fuzzy model is presented. The controller design is posed in an optimisation problem subject to linear matrix inequalities (LMIs) constraints. Multiple positive definite matrices, as a part of the optimisation results, are combined to build a single positive definite matrix that guarantees the stability of the closed-loop system. State feedback controllers are constructed with the optimisation results obtained for each local linear system in the respective fuzzy rule. The controller of the whole system is presented as a fuzzy combination of these local feedback controllers. The controller is then applied to a harmonic drive system which is subject to the non-linear and temperature varying friction. The performance of the controller is verified through the simulation results of tracking reference signals in a temperature varying environment.
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