Singular linear systems with delay: ℋ∞ stabilization

This paper deals with the class of continuous-time singular linear systems with time-delay in the state vector. The stabilization problem of this class of systems using a state feedback controller is tackled. New delay-dependent sufficient conditions on ℋ∞ stabilization are developed. A design algorithm for a memoryless state feedback controller which guarantees that the closed-loop dynamics will be regular, impulse-free and stable with γ-disturbance rejection is proposed. It is shown that the addressed problem can be solved if the corresponding developed linear matrix inequalities (LMIs) with some constraints are feasible. A numerical example is employed to show the usefulness of the proposed results. Copyright © 2007 John Wiley & Sons, Ltd.