Contents 1 Introduction
A descriptor system is a general representation of a physical model in real world since it does not only involve differential equations describing the system evolution, but also the algebraic equations representing certain constraints. During the past decades, the linear descriptor systems theory has been well developed and systematic ways to the analysis and synthesis of linear descriptor systems have been provided [1], [2]. Compared with linear descriptor systems, the development of nonlinear descriptor systems is far from satisfactory. In [3], a series of singular biological models, which are represented by nonlinear descriptor systems with special structure, have been established and qualitative analysis has been performed for them. The stability analysis and state feedback controller design have been studied in [4] for Lur'e descriptor systems. Although a large amount of effort has been made to investigate nonlinear descriptor systems, it is still open how develop the systematic ways to analyze and synthesize a general nonlinear descriptor system. Now the popular way to deal with a general nonlinear system may be the T-S fuzzy method [5]–[7]. When using the T-S fuzzy method, a nonlinear descriptor system can be approximated or exactly represented in a compact set containing origin by a weighted sum of a set of linear descriptor systems with respect to the fuzzy membership functions. In terms of this representation, the existing methods in linear descriptor systems and fuzzy logic fields can be recalled to analyze and synthesize the nonlinear descriptor system. Then the stability analysis and feedback controller design can be cast into the feasibility problems of a set of linear matrix inequalities, which can be solved conveniently. Due to these advantages, T-S fuzzy descriptor systems have found many applications, such as, the inverse dynamics joint torques estimation in human stance [8], motion control of planar parallel robot [9] and biological systems [10], [11].
