Optimal linear quadratic control in the class of output feedbacks

The method of linear matrix inequalities can be successfully applied to problems that have not yet been solved by the method of Riccati equations. The importance of this problem is undoubted, since the only output variables that can usually be measured are those whose dimension is less than that of the state vector. The problem of optimal linear quadratic stabilization in the class of output feedbacks for the system is to find a control from the equations that ensures the asymptotic stability of the closed-loop system and minimizes the functional. For the minimum possible value of γthe corresponding control law can be treated as a suboptirnal control in the linear quadratic stabilization problem.