The Recursive Algorithm for the Optimal Static Output Feedback Control Problem of Linear Singularly Perturbed Systems

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