Maintainability of Structures in Nonhomogeneous Markov Systems Under Cyclic Behavior and Input Control

We study the problem of n-step maintainability of the structure in a nonhomogeneous Markov system (NHMS), which undergoes a cyclic behavior of n steps under input control. The family of n-step maintainable structures is determined as a convex hull of $k^n $ points in $\mathbb{R}^k $, where k is the number of states of the NHMS. We also provide applications of the present results to a large British firm and a University system.