@Article{CSOCB2018,
  author = 	 {Cooman, Adam and Seyfert, Fabien and Olivi, Martine and Chevillard, Sylvain and Baratchart, Laurent},
  title = 	 {{Model-Free Closed-Loop Stability Analysis: A Linear Functional Approach}},
  journal = 	 {{IEEE Transactions on Microwave Theory and Techniques}},
  year = 	 {2018},
  volume = 	 {66},
  number = 	 {1},
  pages = 	 {73--80},
  abstract = { Performing a stability analysis during the design of any
               electronic circuit is critical to guarantee its correct
               operation. A closed-loop stability analysis can be performed
               by analyzing the impedance presented by the circuit at a
               well-chosen node without internal access to the simulator. If
               any of the poles of this impedance lie in the complex right
               half-plane, the circuit is unstable. The classic way to
               detect unstable poles is to fit a rational model on the
               impedance.

               In this paper, a projection-based method is proposed which
               splits the impedance into a stable and an unstable part by
               projecting on an orthogonal basis of stable and unstable
               functions. When the unstable part lies significantly above the
               interpolation error of the method, the circuit is considered
               unstable. Working with a projection provides one, at small cost,
               with a first appraisal of the unstable part of the system.

               Both small-signal and large-signal stability analysis can be
               performed with this projection-based method. In the small-signal
               case, a low-order rational approximation can be fit on the
               unstable part to find the location of the unstable poles.
             },
  keywords = { analog circuits, delay systems, Hilbert space, stability analysis }
}