Poly‐quadratic stability of discrete‐time nonlinear systems in Takagi‐Sugeno's form

This paper studies poly‐quadratic stability of nonlinear systems represented by a Takagi‐Sugeno (T‐S) discrete fuzzy model. A system is poly‐quadratically stable when its stability can be verified by a parameter dependent Lyapunov function. There are already some results in this area. This paper, however, presents less conservative results by adopting more slack‐matrix‐variables in the linear matrix inequalities (LMIs). The parallel distributed compensation (PDC) law is utilized in both the analysis and the synthesis problems. The effectiveness of the new results in this paper is validated by a simulation example.