Abstract
This paper presents a sum of squares (SOS) approach to stabilizing control of discrete polynomial
fuzzy systems. The SOS framework presented in this paper offers a new paradigm over the existing
linear matrix inequality (LMI) approaches to discrete Takagi-Sugeno (T-S) fuzzy models. We derive a
stabilizing control design condition based on polynomial Lyapunov functions that contain quadratic Lyapunov
functions as a special case. Hence, the design approach discussed in this paper is more general than
that based on the existing approaches. The condition derived in this paper can be represented in terms of
SOS and are symbolically and numerically solved via the SOSOPT and SeDuMi, respectively. To illustrate
the validity of the design approach, two design examples are provided. The examples show the utility of
our SOS approach.
