This paper deals with the problem of stochastic optimal control for a class
of nonlinear systems subject to Markovian jump parameters. The nonlinearities in the
different jump modes are initially parameterized by multilayer neural networks (MNNs),
which lead to neural Markovian jump systems. A stochastic neural Lyapunov function
(NLF) is used to analyze the stability of the resulting neural control MJSs. Then, based
on this stochastic NLF and the neural model, a linear state feedback controller is designed
to stabilize the closed-loop nonlinear system and guaranteed an upper bound of the system
performance for all admissible approximation errors of the MNNs. The control gains can
be derived by solving a set of linear matrix inequalities. Finally, a single link robot arm
is demonstrated to show the effectiveness of the proposed design techniques.