Sufficient Conditions for the Local Controllability of Systems with Random Parameters for an Arbitrary Number of System States

We obtain sufficient conditions for the existence of a nonanticipating control for linear systems with stationary random parameters. We consider the case of a bounded control and an arbitrary number of system states. We estimate the probability that the system is nonanticipatingly locally controllable on a fixed time interval. We formulate the main assertions in terms of Lyapunov functions, choosing the latter in the class of piecewise continuously differentiable functions.