A lot of modern problems of automatic control are characterized by large dimensions, the presence of uncertainty in the description of the system, the presence of uncontrollable exogenous disturbances, and a number of other factors that complicate the application of classical methods of the control theory. In this regard, the technique of linear matrix inequalities (LMIs) is very promising. The talk is devoted to the results of new studies that significantly develop the LMI technique and use it to solve the applied problems. We consider the application of the LMI technique in three main directions: - we consider the problem of rejection the unknown-but-bounded exogenous disturbances. The LMI technique allows to reduce the controller design straight to the problem of semidefinite programming; - also, we consider a new approach to the design of sparse feedback in linear control systems; it can be interpreted as reduction of the control resource required to handling the system. The problem reduces to the minimization of special matrix norms subject to the LMI constraints; - we propose the LMI-based design procedure which guarantees “as small as possible” deviations in the closed-loop control systems by means of properly chosen linear feedback.