Robust H∞ state feedback control with an α-stability constraint for uncertain time-delay systems

This paper deals with the problem of robust H_∞ state feedback control with the α-stability constraint for linear time-delay systems with norm-bounded parameter uncertainties in all matrices of a state-space representation. The sufficient condition for the existence of the solutions to the problem is presented in terms of one linear matrix inequality (LMI). Through some manipulations and Schur complements, the controller design is reduced to a convex optimization problem. The solutions can be readily obtained using existing LMI Toolbox without pre-selecting any parameter. A numerical example is provided to illustrate the proposed design approach.