Characterising discrete-time linear systems with the “mixed” positive real and bounded real property
In this paper, we present characterisations of linear, shift-invariant, discrete-time systems that exhibit mixtures of small gain-type properties and positive real-type behaviours in a certain manner. These “mixed” systems are already fairly well characterised in the continuous-time domain, but the...
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| Veröffentlicht in: | European journal of control 2014-09, Vol.20 (5), p.259-268 |
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| container_title | European journal of control |
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| creator | Souza, Matheus Griggs, Wynita M. Ordóñez-Hurtado, Rodrigo H. Sajja, S. Shravan K. Lanzon, Alexander Shorten, Robert N. |
| description | In this paper, we present characterisations of linear, shift-invariant, discrete-time systems that exhibit mixtures of small gain-type properties and positive real-type behaviours in a certain manner. These “mixed” systems are already fairly well characterised in the continuous-time domain, but the widespread adoption of digital controllers makes it necessary to verify whether commonly used discretisation procedures preserve the characteristic of “mixedness”. First, we analyse the effects of classical discretisation methods on the “mixed” property using Nyquist methods. A frequency domain feedback stability result is then presented. Finally, we develop a spectral-based characterisation of “mixed” discrete-time systems which provides a practical computational test that can also be applied to the MIMO case. Several examples validate the developed theory. |
| doi_str_mv | 10.1016/j.ejcon.2014.07.002 |
| format | Article |
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| ispartof | European journal of control, 2014-09, Vol.20 (5), p.259-268 |
| issn | 0947-3580 1435-5671 |
| language | eng |
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| source | ProQuest Central UK/Ireland; Alma/SFX Local Collection |
| subjects | Behavior Discrete-time system Eigenvalues Finite frequency bounded realness Finite frequency positive realness Linear system Methods Stability Studies |
| title | Characterising discrete-time linear systems with the “mixed” positive real and bounded real property |
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