Stability and dissipativity theory for nonnegative dynamical systems: a unified analysis framework for biological and physiological systems

被引:149
作者
Haddad, WM [1 ]
Chellaboina, V
机构
[1] Georgia Inst Technol, Sch Aerosp Engn, Atlanta, GA 30332 USA
[2] Univ Missouri, Columbia, MO 65211 USA
基金
美国国家科学基金会;
关键词
nonnegative systems; compartmental models; stability theory; dissipativity theory; linear Lyapunov functions; storage functions; supply rates;
D O I
10.1016/j.nonrwa.2004.01.006
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Nonnegative dynamical system models are derived from mass and energy balance considerations that involve dynamic states whose values are nonnegative. These models are widespread in biological, physiological, and ecological sciences and play a key role in the understanding of these processes. In this paper we develop several results on stability, dissipativity, and stability of feedback interconnections of linear and nonlinear nonnegative dynamical systems. Specifically, using linear Lyapunov functions we develop necessary and sufficient conditions for Lyapunov stability, semistability, that is, system trajectory convergence to Lyapunov stable equilibrium points, and asymptotic stability for nonnegative dynamical systems. In addition, using linear and nonlinear storage functions with linear supply rates we develop new notions of dissipativity theory for nonnegative dynamical systems. Finally, these results are used to develop general stability criteria for feedback interconnections of nonnegative dynamical systems. (C) 2004 Elsevier Ltd. All rights reserved.
引用
收藏
页码:35 / 65
页数:31
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