Design of Unknown Inputs Observer for a Class of Discrete-Time Takagi-Sugeno Descriptor Models

摘要

This paper addresses the problem of simultaneous estimation of unmeasurable states and unknown inputs (UIs) for a class of discrete-time nonlinear descriptor models (DNDMs) described by Takagi-Sugeno (T-S) structure with unmeasurable premise variables. The UIs affect both state and output of the system. The main idea of the proposed design of fuzzy unknown inputs observer (FUIO) is based on the separation between dynamic and static relations in T-S descriptor model. First, the method permitting to separate dynamic equations from static equations is developed. Next, based on the augmented fuzzy model which contains the dynamic equations and the UIs, a new FUIO design in explicit structure is given. The exponential convergence of the state estimation error is studied by using the Lyapunov theory and the stability conditions are given in terms of linear matrix inequalities (LMIs). Finally, an application to a DNDM of a single-link flexible joint robot is presented in order to illustrate the validity and applicability of the proposed method.