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Normalized finite fractional differences: Computational and accuracy breakthroughs

Rafał StanisławskiKrzysztof J. Latawiec — 2012

International Journal of Applied Mathematics and Computer Science

This paper presents a series of new results in finite and infinite-memory modeling of discrete-time fractional differences. The introduced normalized finite fractional difference is shown to properly approximate its fractional difference original, in particular in terms of the steady-state properties. A stability analysis is also presented and a recursive computation algorithm is offered for finite fractional differences. A thorough analysis of computational and accuracy aspects is culminated with...

A study on new right/left inverses of nonsquare polynomial matrices

Wojciech P. HunekKrzysztof J. Latawiec — 2011

International Journal of Applied Mathematics and Computer Science

This paper presents several new results on the inversion of full normal rank nonsquare polynomial matrices. New analytical right/left inverses of polynomial matrices are introduced, including the so-called τ-inverses, σ-inverses and, in particular, S-inverses, the latter providing the most general tool for the design of various polynomial matrix inverses. The applicationoriented problem of selecting stable inverses is also solved. Applications in inverse-model control, in particular robust minimum...

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