On the Takagi-Sugeno model-based state estimation for one class of bilinear systems

Abstract

The paper presents conditions suitable in design of two types of state observers for a class of continuous-time systems, represented by the Takagi-Sugeno fuzzy model with bilinear rule consequence and the set of measurable premise variables. A Luenberger type observer structure, as well as an unknown input based bilinear observer are explored and subsidiary methods are used for their stability analyze. Giving the notion of linear state estimation error dynamics, and exploiting Lyapunov stability theory, the sufficient conditions are outlined in the terms of linear matrix inequalities, to possess asymptotic stable state estimation, irrespective of the input variables. The method generates an observer for each local bilinear model, and compiles the sub-models by inference through the membership functions. Simulation results illustrate the design procedures and demonstrate the specific performances of the proposed methods.