H2 Optimal State-Feedback Control for Systems with Finite Jumps Corrupted by White Noise

The state–feedback H2optimization problem for a class of systems with finite jumps subjected to additive and to multiplicative white noise is considered. It is proved that the optimal solution can be expressed in terms of the stabilizing solution of an appropriate system of coupled Riccati–type equations. An iterative convergent algorithm to compute this stabilizing solution is also presented. The theoretical developments are illustrated by two numerical examples.