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.
Bibliographical noteFunding Information:
Manuscript received May 21, 2009; revised October 20, 2009; accepted January 18, 2010. First published February 8, 2010; current version published April 2, 2010. This work was supported by Institute of Telecommunications, Multimedia, State-of-charge Information Technology, Yonsei University, a Brain Korea 21 Program, Korea.
All Science Journal Classification (ASJC) codes
- Control and Systems Engineering
- Computational Theory and Mathematics
- Artificial Intelligence
- Applied Mathematics