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Limit cycle like asymptotic dynamics in feedback loops with Memory Based Event Triggering

Memory Based Event Triggering (MBET) is a pragmatic approach to reduce the effective sampling rate of a control system. In MBET, periodically sampled state variables and control inputs are encoded such that data transmission takes place only when they change by a value that exceeds a predetermined threshold. This results in a significant reduction of network traffic in Networked Control Systems (NCS). Should MBET encoding result in an asymptotic cyclic behavior (limit cycle like behavior), it would result in a lower bound in the required bandwidth. In this paper, the necessary conditions for the formation of such a cycle are investigated. It is demonstrated analytically as well as through empirical simulations that the main requirement for the occurrence of asymptotic dynamic cycles is a diffeomorphism between a scalar control input and a unique equilibrium point to which the system will converge to for a constant control input.