A Unified Algebraic Approach to Stabilizing Risk-sensitive Control Design

An extended formulation to the risk-sensitive control of discrete-time linear stochastic systems is presented in the paper. The problem considered is formulated as a convex optimization problem where the design procedure relies on a unified algebraic approach. A possible singular task of risk-sensitive minimum variance control is regularized by defining a quadratic constraint on input variables and linear matrix inequalities are outlined to pose a feasible solution. The resulting formulation gives a necessary and sufficient condition for constrained risk-sensitive minimal variance control. An example is presented along with a discussion to illustrate basic characteristics of the proposed method.