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 the state remains nonnegative for all time. This is done in both continuous and discrete time with an aim of applying these results to population modeling. Further to this, we consider forced nonnegative Lur'e systems, that is, Lur'e systems with an additional disturbance, and provide results on input-to-state stability (ISS), again in both continuous and discrete time. We provide necessary and sufficient conditions for a forced Lur'e system to have the converging-input converging-state (CICS) property in a general setting before specializing these results to nonnegative, single-input, single-output systems. Finally we apply integral control to nonnegative systems in order to control the output of the system with the key focus being on applications to population management.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:698987 |
| Date | January 2016 |
| Creators | Bill, Adam |
| Contributors | Logemann, Hartmut |
| Publisher | University of Bath |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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