Infinite horizon quadratic control of linear singularly perturbed systems with small state delays: an asymptotic solution of Riccati-type equations

An infinite horizon linear-quadratic optimal control problem for a singularly perturbed system with multiple point-wise and distributed small delays in the state variable is considered. The set of Riccati-type equations, associated with this problem by the control optimality conditions, is studied. Since the system in the control problem is singularly perturbed, the equations of this set are also perturbed by a small parameter of the singular perturbations. The zero-order asymptotic solution to this set of equations is constructed and justified. Based on this asymptotic solution, parameter-free sufficient conditions for the existence and uniqueness of solution to the original optimal control problem are established.