Optimal stabilisation of a quasilinear stochastic system with controllable parameters

In this paper we construct necessary conditions for the infinite horizon optimal stabilisation problem of a quasilinear stochastic system with controllable parameters. We propose that matrices in system and criterion (in general non-linearly) depend on vector parameter to be chosen. A particular case of this problem is the infinite-horizon LQG-problem for linear system with multiplicative noise and information constraints.