Development of a numerical algorithm for uncoupling constant coefficient state equations of control theory

A new uncoupling algorithm for system differential equations based on the matrix sign function is presented in this paper. Special forms of system equations arising in many classes of system optimization are investigated. The set of n differential equations formed by the states and costates are uncoupled requiring only the integration of one matrix differential equations of the order n/2. Among the special forms considered are the stiff state equations with constant coefficients for which a numerical algorithm is presented. The algorithm groups the system eigenvalues into separated subsets and generates completely uncoupled filter matrices. Several example solutions are developed using the new method to illustrate the outlined procedures and the numerical accuracy.