Numerically robust delta-domain solutions to discrete-time Lyapunov equations

A problem of numerical conditioning of a special kind of discrete-time Lyapunov equations is considered. It is assumed that a discretisation procedure equipped with the zero-order holder mechanism is utilised that leads to the data matrices that are affinely related to the sampling period and matrices that are independent or linearly related to the squared sampling period. It is shown that common forward shift operator techniques for solving these equations become ill-conditioned for a sufficiently small sampling period and that numerical robustness and reliability of computations can be significantly improved via utilising the so-called delta operator form of the origin equations. (C) 2002 Elsevier Science B.V. All rights reserved.