Contents I. Introduction
Tagaki–Sugeno (T–S) fuzzy model [1]– [4] has received a great deal of attention in control system research area. This model has provided another way to solve the problems of nonlinear control systems. Therefore, many theories and control design methods for linear control systems can be applied in the T–S fuzzy system. In addition, a new approach for designing an optimal coordination controller based on the adaptive fuzzy dynamic programming and game theory for solving the consensus problem of multiagent differential games was studied in [5]. There was a book [6] to study the Type-2 fuzzy logic in detail and a related study to design an adaptive slide mode controller for the interval Type-2 fuzzy systems was reported in [7]. In 2009, a more general form of the T–S fuzzy model called the polynomial T–S fuzzy model has been introduced in [8], and an interval Type 2 polynomial fuzzy model was investigated in [9]. This model allows the system matrices containing polynomial forms in its entries instead of only constant forms. With the supporting sum-of-square (SOS) tools in Matlab [10], the polynomial T–S fuzzy system can be considered as an effective tool for modeling nonlinear control systems. Recently, a large number of studies focused on the polynomial T–S fuzzy systems such as controller design, observer design, and stability analysis [8]–[24]. For example, the stability analyses for the polynomial T–S fuzzy systems by employing the multiple Lyapunov function and switching Lyapunov function were investigated in [13] and [14], respectively. Besides, the controller design and observer-based controller design for the polynomial T–S fuzzy system were studied in many papers such as [18] and [21]– [22]. A non-PDC control design for a polynomial T–S fuzzy system by using control Lyapunov function and Songtag's formula was proposed in [18] . The observer-based controllers for the polynomial T–S fuzzy system with immeasurable premise variables were synthesized in [21] and [23]. Lam et al. [22] proposed a new approach for the stability analysis and controller design for a general polynomial T–S fuzzy system in which the polynomial Lyapunov function candidate does not need to satisfy any constraint. Additionally, the controller synthesis for discrete time polynomial T–S fuzzy systems without and with delay time was developed in [19] and [20], respectively. From the aforesaid review, it becomes obvious that the polynomial T–S fuzzy system has been paid attention increasingly and it extends the study scope larger than the conventional T–S fuzzy system does for nonlinear control systems.
