Abstract
It is well known that the linear growth condition is an important assumption for the stochastic differential system, which can ensure that the solution of the stochastic system will not explode at a finite time. However, there exist a lot of highly non-linear stochastic differential systems, which do not satisfy the linear growth condition, i.e. their coefficients cannot be bounded by a linear function. In this study, the existence of the unique global solution is first proved for highly non-linear switched stochastic systems with non-random switching signals, where the linear growth condition is not required anymore. In addition, by using the mode-dependent average dwell time approach and the Lyapunov functions method, the p th moment exponential stability is presented for highly non-linear switched stochastic systems with both stable and unstable subsystems. An illustrative example is provided to show the effectiveness of the developed theoretical results.
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