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

  • Wassim M. Haddad
  • VijaySekhar Chellaboina
Part of the Lecture Notes in Computational Science and Engineering book series (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.

Keywords

Time Delay Time Delay System Supply Rate Compartmental System Compartmental Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Wassim M. Haddad
    • 1
  • VijaySekhar Chellaboina
    • 2
  1. 1.School of Aerospace Engineering, Georgia Institute of TechnologyAtlanta
  2. 2.Mechanical and Aerospace Engineering, University of MissouriColumbia

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