Limit Cycle Analysis in a Class of Hybrid Systems

Antonio Favela-Contreras, Francisco Beltrán-Carbajal, Alejandro Piñón and Angelo Raimondi

Mathematical Problems in Engineering, 2016, vol. 2016, 1-14

Abstract:

Hybrid systems are those that inherently combine discrete and continuous dynamics. This paper considers the hybrid system model to be an extension of the discrete automata associating a continuous evolution with each discrete state. This model is called the hybrid automaton. In this work, we achieve a mathematical formulation of the steady state and we show a way to obtain the initial conditions region to reach a specific limit cycle for a class of uncoupled and coupled continuous-linear hybrid systems. The continuous-linear term is used in the sense of the system theory and, in this sense, continuous-linear hybrid automata will be defined. Thus, some properties and theorems that govern the hybrid automata dynamic behavior to evaluate a limit cycle existence have been established; this content is explained under a theoretical framework.

Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:2981952

DOI: 10.1155/2016/2981952

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