Static Output Feedback Control of Polynomial Takagi-Sugeno Systems using a Sum Of Squares Approach

The static output feedback (SOF) control for continuous-time polynomial Takagi-Sugeno (T-S) systems is solved in this paper. Using a Polynomial Lyapunov Function, sufficient conditions are derived, in the form of sum-of-squares (SOS). Thanks to some special derivations, these conditions do not include neither transformation matrices nor equality constraints, which simplifies the numerical solution. Moreover, the proposed conditions can provide controllers that are less conservative than those derived from existing results. This is illustrated with some examples at the end of the paper, that show the applicability of the proposed design approach.