Stability and dissipativity theory for discrete-time nonnegative and compartmental dynamical systems

Author

Haddad, Wassim M. ; Chellaboina, ViaySekhar ; August, Elias

Author_Institution

Sch. of Aerosp. Eng., Georgia Inst. of Technol., Atlanta, GA, USA

Volume

5

fYear

2001

fDate

2001

Firstpage

4236

Abstract

Nonnegative and compartmental dynamical systems are derived from mass and energy balance considerations that involve dynamic states whose values are nonnegative. These models are widespread in engineering, biomedicine, and ecology. In this paper we develop several results on stability and dissipativity of discrete-time linear and nonlinear nonnegative dynamical systems. Specifically, using linear Lyapunov functions we develop necessary and sufficient conditions for Lyapunov stability and asymptotic stability for nonnegative systems. In addition, using linear storage functions and linear supply rates we develop new notions of dissipativity theory for nonnegative dynamical systems

Keywords

Lyapunov methods; asymptotic stability; discrete time systems; nonlinear systems; stability criteria; Lyapunov stability conditions; asymptotic stability conditions; biomedicine; discrete-time compartmental dynamical systems; discrete-time nonnegative dynamical systems; dissipativity theory; ecology; energy balance; engineering; linear Lyapunov functions; linear storage functions; linear supply rates; mass balance; necessary and sufficient conditions; stability; stability criteria; Aerodynamics; Aerospace engineering; Asymptotic stability; Biological system modeling; Environmental factors; Lyapunov method; Nonlinear equations; State-space methods; Sufficient conditions; Symmetric matrices;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 2001. Proceedings of the 40th IEEE Conference on

Conference_Location

Orlando, FL

Print_ISBN

0-7803-7061-9

Type

conf

DOI

10.1109/.2001.980857

Filename

980857