Singularly perturbed systems of diffusion type and feedback control

Abstract

Asymptotic approximations describing the behaviour of linear systems of diffusion type (convective or non-convective) with a small diffusivity, to which a feedback control of distributed or boundary type based on point sensors is applied, are constructed and proven to be correct. As a consequence one can find a near-optimal feedback control for a cost minimization problem with a quadratic performance index measuring the deviation of the stationary state from an ideal state, under the restriction of a prescribed exponential degree of stability of the stationary state.