Observer Design for Takagi-Sugeno Descriptor System with Lipschitz Constraints

TL;DR

This paper develops observer design methods for Takagi-Sugeno descriptor systems under Lipschitz constraints, addressing cases with measurable and unmeasurable premise variables, and ensuring convergence via Lyapunov stability and LMIs.

Contribution

It introduces new observer design techniques for TS descriptor systems considering Lipschitz conditions and measurable or unmeasurable premise variables.

Findings

Observer design methods are effective for TS descriptor systems.

Stability conditions are expressed as LMIs.

Examples demonstrate the applicability of the proposed methods.

Abstract

This paper investigates the design problem of observers for nonlinear descriptor systems described by Takagi-Sugeno (TS) system; Depending on the available knowledge on the premise variables two cases are considered. First a TS descriptor system with measurables premises variables are proposed. Second, an observer design which satisfying the Lipschitz condition is proposed when the premises variables are unmeasurables. The convergence of the state estimation error is studied using the Lyapunov theory and the stability conditions are given in terms of Linear Matrix Inequalities (LMIs). Examples are included to illustrate those methods.