Dissipativity‐based adaptive integral sliding mode control of Takagi‐Sugeno fuzzy descriptor systems

This paper focuses on the problem of adaptive integral sliding mode control (ISMC) with dissipativity for a type of complex non‐linear system represented by Takagi‐Sugeno (T‐S) fuzzy descriptor models. First, T‐S fuzzy descriptor systems with different derivative matrices are transformed into augmented systems that have the same properties as the original systems, and an integral sliding mode surface function is designed considering the descriptor matrices. Then, based on the dissipativity theory and the non‐parallel distributed compensation (non‐PDC) method, ISMC strategies and dissipativity‐based ISMC strategies are proposed, and the system uncertainties and external disturbances with unknown upper bounds are addressed with an adaptive controller. According to the Lyapunov theory and the dissipativity theory, a fuzzy Lyapunov function is designed, and the obtained criteria are presented in the form of strict linear matrix inequalities (LMIs); this approach guarantees that the closed‐loop system is asymptotically stable and strictly (Q,R,S)−α$(\mathcal{Q},\mathcal{R},\mathcal{S}) - {{\alpha}}$ dissipative. Moreover, the controller gain matrices and Lyapunov matrices are decoupled by introducing the corresponding auxiliary variables and employing Finsler's lemma. Finally, two examples are provided to illustrate the effectiveness and merit of the proposed method.