# An Adaptive Observer Design for Takagi-Sugeno type Nonlinear System

## TL;DR

This paper introduces an adaptive observer design for Takagi-Sugeno nonlinear systems with unknown parameters, reducing computational complexity and integrating state and parameter estimation.

## Contribution

It presents a novel adaptive observer approach that simplifies computation and unifies state and parameter estimation for T-S systems with unknown parameters.

## Key findings

- Improved observer design reduces computational burden.
- Unified framework for state and parameter estimation.
- Validated with simulation example.

## Abstract

Takagi-Sugeno (T-S) type of polytopic models have been used prominently in the literature to analyze nonlinear systems. With the sector nonlinearity approach, an exact representation of a nonlinear system within a sector could be obtained in a T-S form. Hence, a number of observer design strategies have been proposed for nonlinear systems using the T-S framework. In this work, a design strategy for adaptive observers is presented for a type of T-S systems with unknown parameters. The proposed approach improves upon the existing literature in two folds: reduce the computational burden and provide an algorithmic procedure that would seamlessly connect the state estimation and parameter estimation parts of the observer design. Lyapunov approach is used for the stability analysis and the design procedure. The results are illustrated on a simulation example.