Risk-averse control of linear stochastic systems with low sensitivity: A state-feedback paradigm

The problem of controlling stochastic linear systems with quadratic criterion which includes sensitivity variables is investigated. It is proved that the optimal full state-feedback control law with risk aversion can be realized by the cascade of mathematical statistics of performance uncertainty and a linear feedback. A set of nonlinear matrix equations are obtained, which constitutes the necessary and sufficient conditions that must be satisfied for an optimal solution.