  This paper introduces the notions of stability, ultimate boundedness, and
positive invariance for stochastic systems in the view of risk. More
specifically, those notions are defined in terms of the worst-case Conditional
Value-at-Risk (CVaR), which quantifies the worst-case conditional expectation
of losses exceeding a certain threshold over a set of possible uncertainties.
Those notions allow us to focus our attention on the tail behavior of
stochastic systems in the analysis of dynamical systems and the design of
controllers. Furthermore, some event-triggered control strategies that
guarantee ultimate boundedness and positive invariance with specified bounds
are derived using the obtained results and illustrated using numerical
examples.
