A small gain theorem for linear stochastic systems

A well-known result in linear control theory is the so-called ''small gain'' theorem stating that if given two plants with transfer matrix functions T-1 and T-2 in H-infinity such that parallel to T-1 parallel to < gamma and parallel to T-2 parallel to < 1/gamma, when coupling T-2 to T-1 such that u(2) = y(1) and u(1) = y(2) one obtains an internally stable closed system. The aim of the present paper is to describe a corresponding result for stochastic systems with state-dependent white noise. (C) 1997 Elsevier Science B.V.