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.

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