Limit 2-Cycles for a Discrete-Time Bang-Bang Control Model

Chengmin Hou and Sui Sun Cheng

Discrete Dynamics in Nature and Society, 2012, vol. 2012, 1-10

Abstract:

A discrete-time periodic model with bang-bang feedback control is investigated. It is shown that each solution tends to one of four different types of limit 2-cycles. Furthermore, the accompanying initial regions for each type of solutions can be determined. When a threshold parameter is introduced in the bang-bang function, our results form a complete bifurcation analysis of our control model. Hence, our model can be used in the design of a control system where the state variable fluctuates between two state values with decaying perturbation.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:735623

DOI: 10.1155/2012/735623

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