Generalization of guaranteed cost control-extension to the case with cross terms

This note extends guaranteed cost control based on the linear upper bound to the case with cross product terms in the performance index and shows that the design problem can result in the solvability of the stochastic algebraic Riccati equation with cross product terms (SARECP). It is shown that there exists a solution under stabilizability, detectability and the assumption that the system perturbations and cross terms are not too large.