Residual bounds for discrete-time Lyapunov equations

This paper presents a novel backward error criterion together with a sensitivity measure for assessing the solution accuracy of discrete-time Lyapunov equations. The conventional method involves standard perturbation and sensitivity results for certain associated linear systems. Such an approach, however, ignores the structure of the linear system and is often inconclusive. The method considered in this paper takes full account of the underlying structure of the problem and provides a meaningful measure of accuracy