Object structure

Title:

Recent developments in 2D positive systems theory

Subtitle:

Recent Developments in Two-Dimensional Linear Systems Theory

Group publication title:

AMCS, volume 7 (1997)

Creator:

Fornasini, Ettore ; Valcher, Maria Elena

Subject and Keywords:

sterowanie ; sterowanie-teoria ; sztuczna inteligencja ; matematyka stosowana ; informatyka

Abstract:

Two-dimensional (2D) positive systems are 2D state space models whose variables take only nonnegative values and, hence, are described by a family (A, B, M, N, C, D) of nonnegative matrices. In the paper, the notions of asymptotic and simple stability, corresponding to an arbitrary set of nonnegative initial conditions, are introduced and related to the spectral properties of the matrix sum A + B. ; Some results concerning the positive realization problem for 2D rational functions are also presented. 2D compartmental models are introduced as 2D positive systems which obey some conservation law, and consequently are characterized by the property that the matrix pair (A, B), responsible for their state-updating, has a substochastic sum. ; A canonical form to which every 2D compartmental model can be reduced is derived here, thus leading to obtaining interesting results about stability and positive realizability problems. The relevance of these models is illustrated by means of a couple of examples.

Publisher:

Zielona Góra: Uniwersytet Zielonogórski

Contributor:

Kaczorek, Tadeusz - ed.

Date:

1997

Resource Type:

artykuł

Pages:

713-735

Source:

AMCS, volume 7, number 4 (1997)

Language:

eng

Rights:

Biblioteka Uniwersytetu Zielonogórskiego