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Numerically robust delta-domain solutions to discrete-time Lyapunov equations. (English) Zbl 1106.65314
Summary: A problem of numerical conditioning of a special kind of discrete-time Lyapunov equations is considered. It is assumed that a discretization procedure equipped with the zero-order holder mechanism is utilized 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 utilizing the so-called delta operator form of the origin equations.
65F35Matrix norms, conditioning, scaling (numerical linear algebra)
93B40Computational methods in systems theory
93C55Discrete-time control systems
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