Delay-Dependent Approach to Stabilization of Time-Delay Chaotic Systems via Standard and Delayed Feedback Controllers

In this paper, the stabilization problem of time-delay chaotic systems via standard feedback control (SFC) and delayed feedback control (DFC) methods is investigated. First, new delay-dependent conditions for stabilization via SFC method are obtained in terms of matrix inequalities. The proposed feedback controller stabilizes an unstable equilibrium point in the chaotic system. Then, based on this, delay-dependent conditions for stabilization via DFC method are derived. In both the SFC and DFC cases, algorithms on the design of desired state feedback controllers are proposed. Examples are provided to show the effectiveness of the proposed methods.