On Existence and Stability of Equilibria of dc LTI Circuits with Constant Power Loads

Nikita Barabanov (1) , Romeo Ortega (2) , Robert Grino (3) , Boris Polyak (4)

1 NDSU - North Dakota State University
2 L2S - Laboratoire des signaux et systèmes
3 UPC - Universitat Politècnica de Catalunya = Université polytechnique de Catalogne [Barcelona]
4 Skoltech - Skolkovo Institute of Science and Technology [Moscow]

This paper studies the problem of existence and stability of equilibria of dc linear time-invariant circuits with constant power loads. First, we correct an unfortunate mistake in our previous work [10] 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 equiibria. 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.

Domaines: Automatique

Nikita Barabanov, Romeo Ortega, Robert Grino, Boris Polyak. On Existence and Stability of Equilibria of dc LTI Circuits with Constant Power Loads. 15th European Control Conference (ECC 2016), Jun 2016, Aalborg, Denmark. ⟨10.1109/ECC.2016.7810504⟩. ⟨hal-02378521⟩