The recursive algorithm for the optimal static output feedback control problem of linear singularity perturbed systems

A recursive algorithm is developed for solving the algebraic equations comprising the solution of the optimal static output feedback control problem of singularly perturbed linear systems. The algorithm is very efficient from the numerical point of view, since only low-order systems are involved in algebraic calculations and the required solution can be easily obtained up to an arbitrary order of accuracy, that is O(ε^k) where ε is a small perturbation parameter. The real-world example demonstrates the failure of O(ε) theory used so far in the study of this problem and the necessity for the existence of O(ε^k) theory