H∞ memoryless control with an α-stability constraint for time-delays systems: an LMI approach

This note focuses on the design of H_∞ memoryless state feedback controllers satisfying some α-stability constraints on the closed-loop poles for a class of linear systems with delayed state subject to disturbance inputs. A sufficient condition for feasibility is derived in terms of linear matrix inequalities. Furthermore, the author also considers a particular optimization problem: the maximal bound allowed on time-delay such that the prescribed level on disturbance attenuation and the α-stability constraints are still preserved. This problem is converted into an LMI optimization problem and the author gives a suboptimal bound on the delay