Control of linear systems subjected to exogenous disturbances: combined feedback

A new approach is proposed to the rejection of bounded exogenous disturbances in linear control systems via use of the so-called combined feedback of the form $u=Kx+K_1w$. Along with the static linear state feedback, this control law contains a linear feedback from the vector of disturbances (or some of its components) whose instantaneous values are assumed to be available. The control design procedure is based on the linear matrix inequality technique; it is characterized by simplicity and ease of implementation and reduces to solving convex optimization problems. The combined feedback design is also performed in the sparse formulation, which can be thought of as a desire to reduce the control resource required to handle the system.