Cyclic control equilibria for switched systems with applications to ecological systems

Abstract

The main contribution of this article is to provide the key concept—from a control point of view—of a region of the state space called cyclic control equilibria, which is a permanence region for switched systems under arbitrary waiting-time constraints. The study also includes a discussion about the typical permanence regions (steady-states, multiple equilibria, and invariant sets), and the reasons why these regions (except for the origin) fail to be useful as a control target for switched systems under waiting-times constraints. The theoretical results and the proposed algorithm to compute cyclic control equilibria are tested via illustrative examples. Also, simulation results concerning the control of a population ecological system are given, where it is shown that the ecological communities can be stabilized at desired regions out of the origin, by means of sequences of modes that fulfill arbitrary waiting-time constraints.