Averaged dynamics and pole assignment for a class of stochastic systems

For a linear system with Markov jump parameters, the moment Liapunov exponents are computed explicitly in terms of averaged dynamics. Besides giving a necessary and sufficient condition for moment stability, the computation suggests that control design for these systems can be aimed at assigning desired closed-loop eigenvalues. This is shown to be equivalent to a decentralized control problem to which the homotopy method applies and the control gains are obtained by continuation from the solution of the decoupled (no jump) problem.