The steady states of isotone electric systems

Abstract

The steady states of an isotone electric system are described by an isotone function with respect to the componentwise order. When there are steady states, we highlight a dominant steady state and we study its domain of attraction for the fixed point iteration method.

The Steady States of Isotone Electric Systems

“…Also, S • S is bounded from above. From Theorem 2.5, [3], when Φ S•S ̸ = ∅, there exists y 2 S•S , the dominant fixed point of S • S. This special fixed point of S • S dominates all ω-limit points of S • S (for the fixed point iteration method). In what follows we present some properties of the function S • S.…”

“…In this paper we call the above system the electric power system. As a first example, we specify that the steady states of a linear time invariant DC system with CPLs, see [1] and [3], are the solutions (y, u) ∈ R n × R n of the problem…”

“…y . In the paper [3] we studied the isotone electric system case characterized by the condition that M is a nonnegative matrix. The solutions of the isotone electric system are the fixed points of an isotone function with respect to the componentwise order 4 "≤" on R n .…”

“…In Section 2 we present some properties of the fixed points of a continuous, antitone function S : R * + n → R n . When S is bounded from below by a positive vector, we use our study [3] on the fixed points of a continuous isotone function to prove the existence of a fixed point. In this case, the set of continuous antitone functions is divided into the set of type I functions and the set of type II functions.…”

The steady states of antitone electric systems

“…In this paper, we call the above system the electric power system. As a first example, we specify that the steady states of a linear time invariant DC system with CPLs, see [1] and [2], are the solutions (y,u) ∈ R n × R n of the problem…”