H Control of Linear Singularly Perturbed Systems with Small State Delay

An infinite horizon H state-feedback control problem for singularly perturbed linear systems with a small state delay is considered. An asymptotic solution of the hybrid system of Riccati-type algebraic, ordinary differential, and partial differential equations with deviating arguments, associated with this problem, is constructed. Based on this asymptotic solution, conditions for the existence of a solution of the original H problem, independent of the singular perturbation parameter, are derived. A simplified controller with parameter-independent gain matrices, solving the original problem for all sufficiently small values of this parameter, is obtained. An illustrative example is presented.