Proportional multi-integral observer design for Takagi–Sugeno systems with unmeasurable premise variables: Conservatism reduction via polyquadratic Lyapunov function

Abstract

In this paper, we present the design of a new unknown-input observer for Takagi–Sugeno fuzzy systems with unmeasurable premise variables. The work proposes an improvement of the simultaneous state and unknown-input observer. The main idea is to consider a non-quadratic Lyapunov function in order to reduce the conservatism of its quadratic counterpart. Moreover, the mean value theorem is used to express the error dynamics in a way that reduces the conservatism of the bounded terms assumptions. The stability conditions are formulated as Bilinear Matrix Inequalities. To address these, we propose an iterative algorithm based on linear matrix inequalities, which transforms the Bilinear form into a sets of linear matrix inequalities. Finally, two examples are given to highlight the performance of the proposed observer.