Non‐linear estimation and observer‐based output feedback control

In this study, a new observer is proposed for a class of non‐linear systems which is based on an output‐dependent Riccati equation. Necessary conditions for convergence of the state estimation to the system state are investigated through a theorem. Then, based on the proposed observer, two techniques are developed to solve non‐linear stabilisation and non‐linear tracking problems. It is shown that the separation principle between the estimation and control holds. Indeed, just like a linear system, a decentralised observer‐based state feedback controller can be designed for the non‐linear system while the stability of the closed‐loop system is guaranteed. For the tracking problem, it is proved that the closed‐loop system states converge asymptotically to the states of the desired model. Numerical simulations are given to demonstrate the effectiveness of the proposed observer and the observer‐based controllers.