Attractivity of unstable equilibria for a controlled Chen system via small output feedback

Abstract

We present an output feedback controller for a single-input single-output variant of the Chen dynamical system that renders an unstable equilibrium point of the unforced system attractive using small control signals. The controller first exploits ergodicity of the unforced dynamics to asymptotically estimate the system’s state vector. Then, based on the proximity of the estimate to the desired equilibrium and a computable minimum wait time, a second stage begins applying static output error feedback. Attractivity is proven using interconnected system theory and Lyapunov analysis.