The LaSalle stability theorem of general stochastic hybrid systems
This paper deals with the LaSalle stability theorem of general stochastic hybrid systems. In general the hybrid systems have discontinuous trajectories. And such property brings some difficulty in stability analysis. To overcome this difficulty a new concept named by finite-extraction systems is proposed. For finite-extraction systems their trajectories vary little in a very short time. Depending on this concept and the extended generator formula for GSHS, the LaSalle stability Theorem is extended to general stochastic hybrid systems.