Sensitivity analysis of the discrete-time algebraic Riccati equation Original Research Article

Consider the discrete-time algebraic Riccati equation (DARE) imageATXA−X−(ATXB+S)(R+BTXB)−1(BTXA+ST)+Q=0, where A set membership, variant imagen×n, B, S set membership, variant imagen×m, R = RT set membership, variant imagem×m, Q = QT set membership, variant imagen×n. The available perturbation theory for the DARE can only be applied to the case R > 0. However, in some control problems the matrix R can be singular. In this paper we study perturbation properties of the DARE without the restriction R > 0. Perturbation bounds and a relative condition number for the stabilizing solution of the DARE are derived. Computable residual bounds for an approximate solution are also derived. The theoretical results are illustrated by numerical examples.