Conservatism reduction for Nonlinear Takagi-Sugeno Observer : Interconnected System Approach

Abstract

This work considers observer design for nonlinear systems by using Takagi-Sugeno (TS) models combined to the interconnected systems formalism. The approach is based, on a TS models of interconnected parts obtained from an adequate decomposition of the initial nonlinear system into subsystems, and then transforming each one into Takagi-Sugeno's representation.The observer design conditions for this new representation are expressed as Linear Matrix Inequality (LMI) constraints obtained from a common quadratic Lyapunov functions for stability analysis. The proposed observer, Luenberger-like structure, aims to reduce the number of LMIs and then reduces the conservatism related to the huge number of verticies in the polytope. Numerical examples show the effectiveness of the proposed approach.