PARAMETRIZATION METHOD FOR CALCULATING EXACT STABILITY BOUNDS OF STOCHASTIC LINEAR-SYSTEMS WITH MULTIPLICATIVE NOISE

For deterministic time-invariant linear systems, stability results are quite simple. For stochastic systems, however, even for linear ones, they are rather complicated. In this paper, some results on second mea n stability (mean square stability) of time-invariant linear systems w ith multiplicative noise are summarized and the parametrization method of getting an exact bound for pth mean stability (p greater than or e qual to 2) via second mean stability is stated. Moreover, relations be tween pth mean stabilities for various values of p are given. On the b asis of these relations, a simpler method for getting sufficient condi tions for Pth mean stability is also given, though the resulting suffi cient bound is, of course, more conservative. Comparative studies of v arious conditions are made by using examples. Copyright (C) 1996 Elsev ier Science Ltd.