Solvability and sensitivity analysis of polynomial matrix equation Xs + ATXtA = Q

In this paper, we present a sufficient condition for the existence of the symmetric positive definite solution of polynomial matrix equation Xs + ATXtA = Q where s, t are both nonnegative integers, A,Q∈Rn×n and Q > 0. We firstly define the condition number of the unique SPD solution and reduce its representation form. We also give the algebraic perturbation analysis of the unique SPD solutions with respect to perturbations of matrices A and Q.