A linear-quadratic control problem for state-delay systems. Exact solutions for the Riccati equations

Explicit solutions of linear-quadratic control problems for hereditary syst ems in phase variables are determined by a method based on the generalized quadratic quality functional. For suitably chosen parameters of the quality functional, the generalized Riccati equations defining the coefficients of the optimal linear controller yield to solution in explicit form. Stabiliz ing properties of the controller are studied.