Multiplicative Stochastic Systems with Multiple External Disturbances

Abstract

With the methods of H₂/H_∞-control theory, in the presence of noise we solve the optimization problem for a multiplicative stochastic system with several external disturbances (the multiperturbation problem) and vector Wiener processes with arbitrary intensity matrices. We obtain matrix differential equations of Riccati type, reducing the original optimization problem to solving these equations.