  In this paper, we investigate the mean-square stabilization for discrete-time
stochastic systems that endure both multiple input delays and multiplicative
control-dependent noises. For such multi-delay stochastic systems, we for the
first time put forward two stabilization criteria: Riccati type and Lyapunov
type. On the one hand, we adopt a reduction method to reformulate the original
multi-delay stochastic system to a delay-free auxiliary system and present
their equivalent proposition for stabilization. Then, by introducing a
delay-dependent algebraic Riccati equation (DDARE), we prove that the system
under consideration is stabilizable if and only if the developed DDARE has a
unique positive definite solution. On the other hand, we characterize the
delay-dependent Lyapunov equation (DDLE)-based criterion, which can be verified
by linear matrix inequality (LMI) feasibility test. Besides, under some
restricted structure, we propose an existence theorem of delay margin and more
importantly, derive an explicit formula for computing its exact value.
