Stability of switching linear systems with switching signals driven by stochastic processes

This paper presents conditions to assure the exponential stability in probability for autonomous switching linear systems. The switching signal acting on the autonomous system produces intervals that follow independent, identically distributed stochastic processes—the stability then follows by verifying simple-to-check linear matrix inequalities.     

Stabilizing two-dimensional stochastic systems through sliding mode control

This paper presents a stabilizing control for two-dimensional stochastic differential equations. The stability concept in this study is the stability in probability. To ensure such a stability, the control is designed based on the sliding mode technique, and applied to account stochastic systems. This finding has a practical implication—the proposed control can be used to stabilize a real-time automotive electronic throttle valve. The proposed approach is verified by data collected from experiments.