Discrete optimal control with eigenvalue assigned inside a circular region

A discrete-time optimal control that guarantees that all the closed-loop poles will lie inside a circle centered at (
\beta, 0
) with radius α is formulated. It is shown how the exposed problem can be reduced to a standard discrete-time linear quadratic regulator problem. Furthermore, a quantitative measure of the robustness of linear quadratic state feedback design in the presence of a perturbation is obtained. Bounds are derived for allowable nonlinear perturbations such that the resultant closed loop is stable.