Dynamic output-feedback control for singular T–S fuzzy systems using fuzzy Lyapunov functions

In light of fuzzy weighting-dependent Lyapunov functions, a dynamic output-feedback control for singular T–S fuzzy systems is introduced. Based on a set-equivalence technique and fuzzy weighting-dependent Lyapunov functions, this paper derives a sufficient condition ensuring the singular T–S fuzzy systems to be admissible (regular, impulse-free and stable) in the form of strict parametric linear matrix inequalities (PLMIs). Then, for the closed-loop systems with a dynamic, rather than static, output-feedback controller, an admissibility criterion is given with strict PLMIs by specially representing the block entries of matrices in Lyapunov function. By appropriately choosing the structures of PLMI variables, the strict LMIs are obtained, where slack variables are included in the relaxation process fully exploiting the properties of the fuzzy weighting functions. Three numerical examples are provided to show the effectiveness of the introduced dynamic control.