Stochastic Stability Of Stochastic Differential Systems With Semi-Markovian Switching And Jump

Switched differential systems is used more and more broadly in the fields of physics, engineering technology, biology and economic etc. Stability is an important dynamic indi-cator and one of the main orientations of engineering design.As with the development of industry, more elaborated work are needed in the area of switched stochastic differential systems. In this paper, the stability of switched stochastic and jump differential systems whose switching signal is a semi-Markov process are investigated. Firstly, this kind of system is transformed to Markov processes and their generators are defined under suitable conditions. Secondly, some sufficient conditions for their exponential stability are given. The conclusions consist of theories of switched stochastic differential systems and the re-sults produced by research group headed by Hou Zhenting.