Stabilization of stochastic hybrid systems

The authors address a stabilization scheme for a hybrid system whose state equations are governed by a stochastic switching process, which is modeled as a continuous-time finite-state Markov chain. The proposed linear control law switches its gain based on the imperfectly detected states of the Markov chain. It is assumed that the correct detection probability is the same for all Markov states. The range of the correct detection probability of the detector is computed by solving the conditions for the almost sure sample sure sample path stability of the closed-loop system. Two simple examples are provided to illustrate the technique