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

Abstract EN

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.