New nonlinear observer by state-dependent Sylvester equation approach

In this report, we propose a new approach for nonlinear observer design based on state-dependent Sylvester equation (SDSE). To achieve the state estimation in a nonlinear system, we utilize state-dependent coefficient (SDC) matrices and analytic solutions of the the Sylvester equation. It will be shown that the proposed method extends the linear Luenberger observer formulation to nonlinear systems by using SDC matrices. Due to the analytic solutions for the Sylvester equation, the proposed design method does not rely on numerical computation unlike existing methods such as state-dependent Riccati equation approach, or extended Kalman filter. We verify the effectiveness of the proposed method by numerical simulations and an experiment using a Lorenz-chaos based system.