Observer Design for Takagi-Sugeno Lipschitz Systems Affected by Disturbances using Quadratic Boundedness

In this paper, a proportional observer design using quadratic boundedness is proposed in order to estimate the state of a system described by a Takagi-Sugeno model with a Lipschitz nonlinearity term, and affected by unknown disturbances. The conditions for ensuring that the error between the real and the estimated state converge within an ellipsoidal region about zero, are provided in the form of a linear matrix inequality (LMI) formulation. Then, the simulation results of this approach applied to a four-wheeled omni-directional mobile robot will be shown.