A new approach to robust and non-fragile H∞ control for uncertain fuzzy systems

This paper investigates the robust H∞ control and non-fragile control problems for Takagi–Sugeno (T–S) fuzzy systems with linear fractional parametric uncertainties. The robust H∞ control problem is to design a state feedback controller such that the robust stability and a prescribed H∞ performance of the resulting closed-loop system is ensured. And the non-fragile H∞ control problem is to design a state feedback controller with parameter uncertainties. Based on the linear matrix inequality (LMI) approach, new sufficient conditions for the solvability of the two problems are obtained. It is shown that the desired state feedback fuzzy controller can be constructed by solving a set of LMIs. Numerical examples are also provided to demonstrate the effectiveness of the proposed design method.