New variants of explicit solutions of generalized Riccati equations (Q2709185)

In the linear quadratic control theory for systems with delays there exists a mathematical problem for finding explicit solutions to a system of Generalized Riccati Equations (GREs) which consists of an algebraic matrix equation, an ordinary differential equation, a partial differential equation. In [\textit{A. V. Kim} and \textit{A. B. Lozhnikov}, Linear quadratic problem for the systems with state-delay. Exact solutions of Riccati equations, Avt. itelemekh., No. 7 (2000)] an approach for finding explicit solutions of GREs are proposed. The paper presents new variants of explicit solutions obtained based on this approach.