Abstract This paper considers the problem of robust H∞ control of linear systems with norm-bounded, time-varying, uncertainties in the system and input matrices. Necessary and sufficient conditions are derived that guarantee quadratic stability with H∞ disturbance attenuation for all admissible uncertainties via static output feedback. Two methods are proposed for the solution of the resulting non-convex problem without guaranteed tractability. When these conditions are satisfied, a formula for the robust H∞ controllers is given. Since dynamic output feedback controllers of fixed order can be reformulated as static output feedback controllers for an equivalent augmented system, the results apply to dynamic output feedback as well. Examples are included to demonstrate the application of the results.
Köse et al. (Sun,) studied this question.