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On positive descriptor systems
Author(s) -
Virnik Elena
Publication year - 2006
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200610406
Subject(s) - decoupling (probability) , ode , lyapunov function , complement (music) , schur complement , mathematics , state vector , function (biology) , computer science , control theory (sociology) , nonlinear system , artificial intelligence , control (management) , chemistry , control engineering , engineering , biology , physics , biochemistry , classical mechanics , quantum mechanics , evolutionary biology , eigenvalues and eigenvectors , complementation , gene , phenotype
When economical, biological or chemical systems are modelled by descriptor systems, in which the state x describes concentrations, populations of species, or numbers of cells, then the solution is a nonnegative vector function. Hence, the numerical methods for the control or simulation should respect this special structure. We define and characterise positivity for descriptor systems. Furthermore, for a special case, we show a Schur complement decoupling technique that reduces a descriptor system to the ODE case. We use this technique to present a characterisation of the existence of positive solutions to generalised Lyapunov equations. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)