H_∞ control for linear systems with additive controller gain variations

This paper is concerned with the problem of linear state feedback _∞ 1 controller design for linear time-invariant systems in the presence of controller gain variations. The controller gain to be designed is assumed to have additive gain variations. A design method is presented in terms of symmetric positive-definite solutions to a parameter-dependent inequality, which degenerates to the standard H_∞ 1 state feedback control designs when the controller gain variations become zero. The designed controller with gain variations is such that the closed-loop system is quadratically stable and has an _∞ 1 disturbance attenuation bound. Numerical examples are given to illustrate the design procedure and its ectiveness.