Υ. A. Phillis, "Controller design of systems with multiplicative noise," IEEE Tran. on Aut. Control, vol. 30, no. 10, pp. 1017-1019, 1985.doi :
10.1109/TAC.1985.1103828
https://doi.org/ 10.1109/TAC.1985.1103828
General linear continuous stochastic systems are considered with multiplicative noise in the control and state channels and stabilizing optimal inputs are synthesized for both time-varying and time-invariant situations. In the nonstationary case, a set of nonlinear matrix differential equations has to be solved. In the stationary problem, a set of nonlinear matrix algebraic equations provides the solution. The separation principle is not valid and both the state filtering and the control synthesis problem should be treated simultaneously.