Frequency conditions in \(H^\infty\)-control and absolute stabilization problems (Q1375018)

It is known that solving Lur'e-Riccati matrix equations in the theory of absolute stability is connected with the existence of a special solution of variational problems with an integral quadratic functional. Frequency inequalities that arise in this theory are existence conditions of solutions to these variational problems. Riccati matrix equations of a special form also arise in investigations on \(H^\infty\)-control. This class of Riccati equations is connected with a minimax problem, and their solution is connected with the presence of a saddle point in the function space in which the minimax problem is embedded. In turn, \(H^\infty\)-control problems intersect with nonlinear absolute stabilization problems. In this paper, the author establishes the frequency inequalities that are existence conditions of solutions for the considered class of \(H^\infty\)-control and absolute stabilization problems.