Two-time-scale system with random parameters

In this paper, a class of two-time scale systems which are subject to sudden changes in parameter values are studied. The systems in which the performance measure is quadratic are investigated. The corresponding Riccati equations are coupled ones. The original system is decomposed into reduced-order slow and fast subsystems. A composite, closed-loop optimal control is created from the sum of the slow and fast feedback optimal controls. The decomposition is independent from the regime transitions. The results are verified through a numerical example