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Nowe perspektywy w analizie żywności

Ulanowska A., Strączyński G.

LAB Laboratoria, Aparatura, Badania

2012

R. 17, nr 4

31-34

An LMI approach to checking stability of 2D positive systems

Twardy M.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2007

Vol. 55, nr 4

385-395

Two-dimensional (2D) positive systems are 2D state-space models whose state, input and output variables take only nonnegative values. In the paper we explore how linear matrix inequalities (LMIs) can be used to address the stability problem for 2D positive systems. Necessary and sufficient conditions for the stability of positive systems have been provided. The results have been obtained for most popular models of 2D positive systems, that is: Roesser model, both Fornasini-Marchesini models (FF-MM and SF-MM) and for the general model.

Algorithm for determining all finite paths in a 2D directed graph

Markowski K.A., Szlenk M., Twardy M.

Przegląd Elektrotechniczny

2006

R. 82, nr 1

50-52

This paper addresses the problem of determining all finite paths in a 2D direct graph. This problem arises when one wants to compute reachability index for two-dimensional positive systems. To accomplish this task a simple algorithm has been proposed. The algorithm consists in decomposition of a 2D digraph into finite paths in which then appropriate arcs are counted. Finally, the proposed algorithm has been illustrated by a numerical example.

Podano metodę wyznaczania dodatnich realizacji minimalnych dla dyskretnych układów jednowymiarowych. Sformułowano warunki wystarczające istnienia realizacji dodatnich oraz podano procedurę wyznaczania tych realizacji dla danej właściwej funkcji wymiernej. Rozważania zilustrowano przykładem numerycznym.

Reachability and minimum energy control of positive 2D systems with delays

Kaczorek T.

Control and Cybernetics

2005

Vol. 34, no 2

411-423

The notion of internally positive 2D model (system) with delays is introduced. Solution of the 2D linear models with delays is derived. Necessary and sufficient conditions for the internal positivity and reachability of the models are established. The Cayley-Hamilton theorem for the 2D linear models with delays is extended. The minimum energy control for the internally positive 2D models with delays is formulated and solved.