Analysis of Separation Principle on Fuzzy Observer-Control System via Homogeneous Lyapunov

In this project, a polynomial nonlinear system, modelled by T-S fuzzy model with added disturbances, is studied. Based on non-quadratic, homogeneous Lyapunov function, both controller and observer are considered in the analysis where Euler's homogeneous polynomial theorem is used to avoid the derivative term \dot Q(x) that is seen in the existing research papers. Furthermore, the principle of separation is investigated to see whether such property holds true in this polynomial structure.We explicitly established the model (plant, controller and observer) mentioned how to approach the problem. Finally, Sum of Square is applied to solve for the Lyapunov Q(x) and controller/observer gains, thereby ensuring the stability of the closed-loop observed-state feedback control system.