Reliable mixed L2/H∞L2/H∞ fuzzy static output feedback control for nonlinear systems with sensor faults

This paper is concerned with the design of reliable mixed L2/H∞L2/H∞ static output feedback (SOF) fuzzy controllers for nonlinear continuous-time systems with complete sensor faults. The Takagi and Sugeno (T–S) fuzzy model is employed to represent a nonlinear system. A sufficient condition for the existence of reliable mixed L2/H∞L2/H∞ SOF fuzzy controllers is presented in terms of a set of quadratic matrix inequalities (QMIs), which not only guarantees that the closed-loop fuzzy system satisfies a desired H∞H∞ disturbance attenuation constraint for all admissible operating regimes (including the normal and sensor fault cases), but also provides different upper bounds on the L2L2 performance criterion for different operating regimes. A suboptimal reliable fuzzy controller is obtained by the proposed iterative linear matrix inequality (ILMI) algorithm for minimizing the normal L2L2 performance bound, while maintaining acceptable lower levels of the bounds in the sensor fault cases. Finally, a numerical example is given to illustrate the effectiveness of the proposed design method.