  For the sake of saving time and costs the feedback control based on
discrete-time observations is used to stabilize the switching diffusion
systems. Response lags are required by most of physical systems and play a key
role in the feedback control. The aim of this paper is to design delay feedback
control functions based on the discrete-time observations of the system states
and the Markovian states in order for the controlled switching diffusion system
(SDS) to be exponentially stable in $p$th moment and probability one as well as
stable in $H_\infty$. The designed control principles are implementable to
stablize quasi-linear and highly nonlinear SDSs. For quasi-linear SDSs the
criteria are sharp that under the control with high strength the controlled
SDSs will be stable (bounded) while under the weaker control they will be
unstable (unbounded) in mean square. The sample and moment Lyapunov exponents
are estimated which have close relationship with the time delays.
