Unknown Input-Based Observer Synthesis for a Polynomial T–S Fuzzy Model System With Uncertainties

Robust observer synthesis for the uncertain large‐scale T–S fuzzy system

“…Owing to the bounded constraints, the magnitude of the uncertainties may be restricted. Although in Assumption 1 the uncertainties need not require to fulfil the bounded constraints, the size of uncertainties in this paper is not limited. Remark 3 It should be noted that the problem of the observer design for the uncertain T–S fuzzy system when the upper bounds of the uncertainties are unknown has been studied in several previous papers [12, 35–37]. However, system (2a) is more complicated with respect to the T–S fuzzy system because it comprises multiple T–S fuzzy subsystems and, especially, the interconnection terms.…”

“…Hence, observer synthesis is considered as an alternative option to overcome these difficulties and has attracted a considerable attention from researchers. Various studies paying attention to the observer design for the T–S fuzzy system have been published in recent years [11, 12, 28–37]. For example, in [11], an observer‐based controller was designed for the uncertain T–S fuzzy system.…”

“…Additionally, the unknown input method was introduced in [32–34] to construct the observer for the unknown input T–S fuzzy system. Furthermore, recently, the approaches based on an unknown input method to synthesise an observer for an uncertain T–S fuzzy system were investigated in [12, 35–37], in which the influences of the uncertainties were eliminated completely, even though their upper bounds were not known. Unfortunately, according to the best of our knowledge, there has not been any previous paper considering the observer synthesis for the uncertain large‐scale T–S fuzzy system when the upper bounds of the uncertainties are unknown.…”

“…Therefore, we are inspired to study further for synthesising an observer for this system. Unfortunately, the large‐scale T–S fuzzy system is more complicated than the T–S fuzzy system because it consists of multiple T–S fuzzy subsystems as well as the interconnection terms, which makes the methods in [11, 12, 28–37] to be unable to apply to design an observer for the uncertain large‐scale T–S fuzzy system. The aforementioned discussions have motivated us to study a new method for synthesising a robust observer to estimate the immeasurable states of the uncertain large‐scale T–S fuzzy systems.…”

Disturbance Observer-Based Linear Matrix Inequality for the Synchronization of Takagi-Sugeno Fuzzy Chaotic Systems

“…The method plays the role of a nonlinear system in mathematical modeling by if-then fuzzy rules and sublinear systems. Due to the rapid development of computer speed, the T-S method has been studied by many papers [19][20][21][22][23][24][25][26][27]. To take advantage of the T-S fuzzy system, the synchronization of the chaotic system has been reconstructed in the form of a T-S system [28][29][30][31][32][33][34].…”