A recently proposed time-varying generalisation of Vinnicombe's ν-gap is shown to have the properties of a metric on a class of causal linear continuous-time systems that admit normalised strong graph representations. An alternative time-varying gap metric is then defined in more general terms and a corresponding robust stability result is derived for linear feedback interconnections. Finally, it is shown that the time-varying gap and ν-gap metrics induce the same topology, this being the coarsest topology under which feedback stability and closed-loop sensitivity are both robust properties.
Bibliographical noteFunding Information:
This work was supported by the Swedish Research Council through the LCCC Linnaeus centre and the Australian Research Council ( DP130104510 ). This paper was not presented at any IFAC meeting.
- Linear time-varying systems
- Robust stability