Stabilization of uncertain fuzzy control systems via a new descriptor system approach

This paper addresses stabilizing a class of fuzzy control systems with a guaranteed H∞H∞ control performance via a new descriptor system approach. Based on the sector nonlinearity concept of Tanaka and Wang (2001) [1], the uncertain nonlinear system can be exactly represented by T–S fuzzy models. Then, we propose using the composite state and output feedback (CSAOF) fuzzy control for the control design. A new descriptor fuzzy system will be represented in this paper. Based on the Lyapunov stability theorem and the linear matrix inequality (LMI) tool, we solve the controller gain matrices, some positive constants and some common positive-definite matrices. Then, we derive two sufficient conditions to stabilize the uncertain fuzzy control systems with guaranteed H∞H∞ control performance. Moreover, the developed H∞H∞ criterion guarantees that the influence of external disturbance is as small as possible. A practical system is given to illustrate the validity of the proposed scheme.