Linear fractional transformation based H-infinity output stabilization for Takagi-Sugeno fuzzy models

Madjid Zerar, Kevin Guelton et Noureddine Manamanni

In this paper, a global stabilization and robust Dynamic Output Feedback Controller (DOFC) design methodology for Takagi-Sugeno (T-S) fuzzy systems is proposed. Based on a standard robust control structure, one rewrites an original nonlinear model as an extended nonlinear model with exogenous inputs. The latter contains control objectives that are classically introduced in terms of linear weighting functions in robust control theory. In order to point out the interconnection between the extended nonlinear model and the designated DOFC, unsolvable stability conditions are derived using Linear Fractional Transformation (LFT) and H¥ tools. Based on the universal approximator properties of T-S modeling, the obtained nonlinear stability conditions are then transformed into Linear Matrix Inequalities (LMI) to allow the design of a dedicated Full Parallel Distributed Compensation (FPDC) DOFC. In that case, when a solution is tractable from the proposed LMI conditions, the synthesized controller guarantees the prescribed stability performances. Finally, a numerical example is used to illustrate the validity of the designed approach.

Mots clés

Takagi-Sugeno Fuzzy Models, Robust Control, Linear Fractional Transformation (LFT), Linear Matrix Inequalities (LMI), H-Infinity.