Linear Matrix Inequalities in Control Problems

Many contemporary automatic control problems are characterized by large dimensions, the presence of uncertainty in the description of the system, the presence of uncontrolled exogenous disturbances, the need to analyze large amounts of information online, decentralization/simplification of control systems in multi-agent systems, and a number of other factors that complicate the application of classical methods of control theory. Therefore, the problem of developing new efficient methods that take into account these specific features becomes topical. In this regard, the technique of linear matrix inequalities is very promising. This paper presents the results of new studies that develop the technique of linear matrix inequalities and use it to solve applied control theory problems.