The inverse problem of linear optimal control for constant disturbance

This paper presents the solution to the inverse problem of linear optimal control systems to achieve pole placement and at the same time minimize the cost function and accommodate a constant but unknown disturbance. The sufficient conditions for an optimal feedback law to have a positive R and positive semi-definite Q are found. The relationships between the open-loop poles and the closed-loop poles that guarantee a positive R and Q ≥ 0 are also obtained. These relations offer a rule for selection of the appropriate closed-loop poles which will guarantee the required feedback properties.