Discrete-time optimal control for linear time-delay systems with deterministic disturbances

This paper presents an approach to formulating the optimisation problem of linear discrete-time systems with delays. It is shown that, by properly augmenting the state vector, the optimisation problem of achieving closed-loop poles inside a circular region with centre (β. 0) and radius α, where α + |β| ≤ 1, and at the same time accommodating deterministic disturbances, can be reduced to a standard discrete quadratic regulator problem with no delays. It is also shown that the dynamical feedback controller, which minimises the performance to achieve poles inside a circular region and accommodate disturbances, can be implemented via an auxiliary linear dynamical system. The implementation scheme is effective in many applications.