Control of Linear Systems Subjected to Exogenous Disturbances: Combined Feedback

A new approach to rejection of exogenous disturbances in linear control systems via static combined feedback is proposed. Namely, in addition to static linear state feedback, we introduce a linear feedback from the components of exogenous disturbances whose instantaneous values are assumed to be known. The control design is based on the technique of linear matrix inequalities, and the proposed simple approach leads to a convex minimization problem. Moreover, a new approach to the design of sparse combined feedback in linear control systems is proposed; it can be interpreted as reduction of the control resource required to handling the system.