Nonlinear stabilization of jump linear Gaussian systems

This paper considers jump linear (JL) systems under the assumption that the mode (system model) is not directly observed. In this situation, the optimal control and stabilization problems are nonlinear (dynamic) optimization problems and very difficult due to the dual effect. Assuming that the base state is perfectly measured, this work answers the following question positively: If the JL system is stabilizable by a linear feedback control, can one find a better stabilizing controller? Two such nonlinear control schemes are presented. For the case of an unknown parameter problem, an example is given to show that the cost from using a nonlinear stabilizing controller derived is within a few percent from a lower bound of the (unknown) optimal cost; and is about half of the cost by using an algorithm from the literature, due to Saridis (1972).