COMPARTMENTAL MODELING AND 2ND-MOMENT ANALYSIS OF STATE-SPACE SYSTEMS

被引：75

作者：

BERNSTEIN, DS ^{[1
]}

HYLAND, DC ^{[1
]}

机构：

[1] HARRIS CORP,MELBOURNE,FL 32902

来源：

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 1993年 / 14卷 / 03期

关键词：

STOCHASTIC MODELS; POWER FLOW; NONNEGATIVE MATRICES;

D O I：

10.1137/0614060

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Compartmental models involve nonnegative state variables that exchange mass, energy, or other quantities in accordance with conservation laws. Such models are widespread in biology and economics. In this paper a connection is made between arbitrary (not necessarily nonnegative) state space systems and compartmental models. Specifically, for an arbitrary state space model with additive white noise, the nonnegative-definite second-moment matrix is characterized by a Lyapunov differential equation. Kronecker and Hadamard (Schur) matrix algebra is then used to derive an equation that characterizes the dynamics of the diagonal elements of the second-moment matrix. Since these diagonal elements are nonnegative, they can be viewed, in certain cases, as the state variables of a compartmental model. This paper examines weak coupling conditions under which the steady-state values of the diagonal elements actually satisfy a steady-state compartmental model.

引用

页码：880 / 901

页数：22

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[11] GEOMETRY OF COUPLED MODE PROPAGATION IN ONE-DIMENSIONAL RANDOM MEDIA [J].