Risk-Aware Stability, Ultimate Boundedness, and Positive Invariance

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