This paper is concerned with the problem of non-fragile H∞ controller design for linear time-invariant systems. The controller to be designed is assumed to have multiplicative gain variations. Design methods are presented in terms of symmetric positive-definite solutions of algebraic Riccati inequalities. The resulting design is such that the closed-loop system is robustly stable and has an H∞ disturbance attenuation bound with respect to the multiplicative controller gain variations. A numerical example is given to illustrate the design methods.