Nonnegative Feedback Systems in Population Ecology

  • Adam Bill

Student thesis: Doctoral ThesisPhD


We develop and adapt absolute stability results for nonnegative Lur'e systems,that is, systems made up of linear part and a nonlinear feedback in which thestate remains nonnegative for all time. This is done in both continuous anddiscrete time with an aim of applying these results to population modeling.Further to this, we consider forced nonnegative Lur'e systems, that is, Lur'esystems with an additional disturbance, and provide results on input-to-statestability (ISS), again in both continuous and discrete time. We provide necessaryand sufficient conditions for a forced Lur'e system to have the converging-inputconverging-state (CICS) property in a general setting before specializingthese results to nonnegative, single-input, single-output systems. Finally weapply integral control to nonnegative systems in order to control the outputof the system with the key focus being on applications to population management.
Date of Award22 Jul 2016
Original languageEnglish
Awarding Institution
  • University of Bath
SupervisorHartmut Logemann (Supervisor)


  • Nonnegative systems
  • Feedback
  • Lur'e
  • Population ecology
  • Input-to-state stability
  • Converging-input converging-state
  • Integral control

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