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Advances in Time-Delay Systems pp 421–435Cite as

Stability and Dissipativity Theory for Nonnegative and Compartmental Dynamical Systems with Time Delay

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Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 38))

Abstract

Nonnegative and compartmental dynamical system models are derived from mass and energy balance considerations that involve dynamic states whose values are nonnegative. These models are widespread in engineering and life sciences and typically involve the exchange of nonnegative quantities between subsystems or compartments wherein each compartment is assumed to be kinetically homogeneous. However, in many engineering and life science systems, transfers between compartments are not instantaneous and realistic models for capturing the dynamics of such systems should account for material in transit between compartments. Including some information of past system states in the system model leads to infinite-dimensional delay nonnegative dynamical systems. In this chapter we present necessary and sufficient conditions for stability of nonnegative and companmental dynamical systems with time delay. Specifically, asymptotic stability conditions for linear and nonlinear as well as continuous-time and discrete-time nonnegative dynamical systems with time delay are established using linear Lyapunov-Krasovskii functionals. Furthermore, we develop new notions of dissipativity theory for nonnegative dynamical systems with time delay using linear storage functionals with linear supply rates. These results are then used to develop general stability criteria for feedback interconnections of nonnegative dynamical systems with time delay.

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Author information

Authors and Affiliations

  1. School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA, 30332-0150

    Wassim M. Haddad

  2. Mechanical and Aerospace Engineering, University of Missouri, Columbia, MO, 65211

    VijaySekhar Chellaboina

Authors
  1. Wassim M. Haddad
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  2. VijaySekhar Chellaboina
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Editor information

Editors and Affiliations

  1. Centre de Recherche de Royallieu, Universite de Technologie de Compiègne, UMR CNRS 6022, 60205, Compiègne, France

    Silviu-Iulian Niculescu

  2. Department of Mechanical and Industrial Engineering, Southern Illinois University, Edwardsville, IL, 62025-1805, USA

    Keqin Gu

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© 2004 Springer-Verlag Berlin Heidelberg

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Haddad, W.M., Chellaboina, V. (2004). Stability and Dissipativity Theory for Nonnegative and Compartmental Dynamical Systems with Time Delay. In: Niculescu, SI., Gu, K. (eds) Advances in Time-Delay Systems. Lecture Notes in Computational Science and Engineering, vol 38. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18482-6_29

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  • DOI: https://doi.org/10.1007/978-3-642-18482-6_29

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20890-7

  • Online ISBN: 978-3-642-18482-6

  • eBook Packages: Springer Book Archive

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