Stabilization of jump linear Gaussian systems

The importance of jump linear (JL) systems in modeling practical physical systems, e.g., tracking, repairable systems, systems subject to abrupt changes etc., has drawn extensive attention. Results have been obtained in control, stabilization and filtering, when the mode (system model) is assumed to be directly and perfectly observable, which, in many applications, is an unrealistic assumption. When this is not the case, the optimal control and the stabilization problems become very difficult due to the dual effect. In this work, the authors assume that the mode is not observable, but the base state is perfectly measured. The authors give a sufficient condition to stabilize a JL system using an “i.i.d. controller” (a controller derived using an i.i.d. assumption for the system mode), a necessary condition of stabilizability and an upper and a lower bound to the optimal cost for a JL system. It is shown that a controller stabilizing the noise-free system also stabilizes the noisy one. An algorithm (and its convergence) to compute the optimal feedback gain for a system with i.i.d. modes is presented