Stationary Response Of Stochastically Excited Nonlinear Systems Undergoing Markovian Jump

Markovian-jump systems represent a class of hybrid systems which involve both continuous and discrete variables. Complex dynamical systems are often Markovian-jump systems because abrupt changes in their configurations may occur due to component or interconnection failure or sudden environmental disturbances. In this thesis, the stationary response of stochastically excited nonlinear Markovian-jump system is investigated based on the stochastic averaging method. Firstly, the averaged Ito stochastic differential equation for each form of the MJSs is obtained by using stochastic averaging method. If the Markovian jump process is a slowly jump process and independent of system states, the original system can be approximately substituted by the averaged Ito stochastic differential equation with Markovian jump. The dimension of the original system is reduced significantly. Then, according to the Markovian jump principle, the finite set of FPK equations associated with the averaged Ito equation can be obtained. They are coupled through the absorptive and reductive terms. The stationary response and its statistics of the MJSs can be obtained by solving the FPK equations numerically. Finally, the theory method is applied to analyze the stationary response of stochastically excited nonlinear single degree-of-freedom (SDOF) and Multi degree-of-freedom (MDOF) quasi-nonintegrable Hamiltonian system with Markov jump. Some examples are worked out in detail to demonstrate the validityand perhaps accuracy of the method presented.