Constrained variance design for bilinear stochastic continuous systems

The aim of the paper is to find a compatible covariance matrix which satisfies the variance constraints on the outputs, then to use the state covariance assignment theory to determine the linear state feedback gain matrix that will meet the variance constraints on the inputs. The paper introduces a theory for the control of the state covariance of time-invariant bilinear stochastic continuous systems. The authors define the necessary and sufficient conditions for the existence of a feedback gain matrix which can assign a specified state covariance to bilinear stochastic systems. Moreover, they find the set of feedback gain matrices such that the closed-loop bilinear system achieves the assigned state covariance. Finally, they develop a methodology of constrained variance designing for bilinear stochastic continuous systems