We study in a dynamical system context the random feedback stabilization problem for linear, random control processes. We are led to study the random linear regulator problem, which we solve by considering the spectral theory of linear time-dependent Hamiltonian systems. This is done with the aid of the concepts of exponential dichotomy and rotation number.
Stabilization and random linear regulator problem for random linear control processes / R. Johnson; M. Nerurkar. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - STAMPA. - 197:(1996), pp. 608-629. [10.1006/jmaa.1996.0042]