On existence and stability of equilibria of linear time-invariant systems with constant power loads - CentraleSupélec Access content directly
Journal Articles IEEE Transactions on Circuits and Systems Year : 2015

On existence and stability of equilibria of linear time-invariant systems with constant power loads

Nikita Barabanov
  • Function : Author
Robert Grino
  • Function : Author
B Polyak
  • Function : Author

Abstract

The problem of existence and stability of equilibria of linear systems with constant power loads is addressed in this paper. First, we correct an unfortunate mistake in our recent paper pertaining to the sufficiency of the condition for existence of equilibria in multiport systems given there. Second, we give two necessary conditions for existence of equilibria. The first one is a simple linear matrix inequality hence it can be easily verified with existing software. Third, we prove that the latter condition is also sufficient if a set defined by the problem data is convex, which is the case for single and two-port systems. Finally, sufficient conditions for stability and instability for a given equilibrium point are given. The results are illustrated with two benchmark examples.
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Dates and versions

hal-01632549 , version 1 (23-06-2020)

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Nikita Barabanov, Roméo Ortega, Robert Grino, B Polyak. On existence and stability of equilibria of linear time-invariant systems with constant power loads. IEEE Transactions on Circuits and Systems, 2015, 63 (1), pp.114-121. ⟨10.1109/tcsi.2015.2497559⟩. ⟨hal-01632549⟩
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