Stability analysis and controller synthesis for fuzzy descriptor systems
This article primarily investigates the stability and controller design of fuzzy descriptor systems. The standard Takagi-Sugeno (T-S) fuzzy model is generalised into a descriptor T-S fuzzy model with the distinct derivative matrices in each rule, which can be used to represent a larger class of nonlinear systems. Based on a derived equivalent stability condition for the nominal descriptor system, the stability of unforced fuzzy descriptor systems with blending different derivative matrices can be treated. Furthermore, parallel distributed compensation (PDC) and a fuzzy proportional and derivative state feedback (PDSF) controller are proposed for stabilising the resulting closed-loop fuzzy descriptor systems. Significantly, all the presented criteria are formulated in terms of linear matrix inequalities (LMIs), so the stability analysis or a stabilising fuzzy controller can be readily achieved via current LMI solvers. Given numerical examples, we demonstrate the effectiveness and merit of the proposed approach.
stability analysis controller synthesis fuzzy descriptor system linear matrix inequality (lmi) t-s model