Derivation of weighting matrices towards satisfying eigenvalue requirements

The present work is concerned with the problem of designing appropriate weighting matrices for the performance index of the linear regulator optimization problem, guch that the resulting optimal policy satisfies given eigenvalue requirements. The text provides an algorithm for deriving a diagonal state-weighting matrix according to these eigenvalue requirements, the latter often being better defined than the requirements for the stato-weighting matrix. The solution given employs matrix differential calculus and a static gradient minimization sub-routine to minimize an eigenvalue error criterion, thus facilitating optimal control within desired eigenvalue requirements.