Improvement on Nonquadratic Stabilization of Discrete-Time Takagi-Sugeno Fuzzy Systems: Multiple-Parameterization Approach

This paper presents the relaxed nonquadratic stabilization conditions of discrete-time Takagi–Sugeno (T–S) fuzzy systems. To do this, we propose a new fuzzy controller and Lyapunov function by generalizing the nonparallel distributed compensation (non-PDC) control law and nonquadratic Lyapunov function, respectively. By exploiting Pólya’s theorem and algebraic properties of a homogeneous polynomials of normalized fuzzy weighting functions, an infinite family of sufficient conditions for the asymptotic stabilizability is derived. These conditions are formulated in the format of linear matrix inequalities (LMIs) and, hence, are numerically tractable via convex programming techniques. Finally, an example is given to illustrate advantages of the proposed method.