The Infinite Time Quadratic Control Problem for Linear Systems with State and Control Delays: An Evolution Equation Approach

Abstract

We show how a linear differential delay equation with delays in the control can be reformulated as an evolution equation with bounded input operator. As a simple application, we solve an infinite time quadratic cost control problem for the delay differential equation. We also point out how our results, even when specialized to the case where delays in the control disappear, extend results previously published in the literature.