Stochastic H2 Optimal Control for a Class of Linear Systems with Periodic Coefficients

This paper presents an optimal solution of the H2 statefeedback control problem for time-varying periodic stochastic linear systems subject to both jump Markov perturbations and multiplicative white noise. It is proved that the optimal solution is a static gain which is also optimal in the class of all higher order controllers. This solution is expressed in terms of the stabilizing solution of some generalized coupled Riccati type differential equations. An iterative procedure which allows us to compute the stabilizing solution of the corresponding generalized Riccati differential equation is proposed.