Brief paper: state estimation of Takagi-Sugeno systems with unmeasurable premise variables

This study is dedicated to the design of observers for non-linear systems described by Takagi-Sugeno (T-S) multiple models with unmeasurable premise variables. Furthermore, this T-S structure can represent a larger class of non-linear systems compared to the T-S systems with measurable premise variables. Considering the state of the system as a premise variable allows one to exactly represent the non-linear systems described by the general form x¿ = f(x, u). Unfortunately, the developed methods for estimating the state of T-S systems with measured premise variable are not directly applicable for the systems that use the state as a premise variable. In the present paper, firstly, the design of observers for T-S systems with unmeasurable premise variable is proposed and sufficient convergence conditions are established by Lyapunov stability analysis. The linear matrix inequality (LMI) formalism is used in order to express the convergence conditions of the state estimation error in terms of LMI and to obtain the gains of the observer. Secondly, the proposed method is extended in order to attenuate energy-bounded unknown inputs such as disturbances. An academic example is proposed to compare some existing methods and the proposed one.