<p>The dielectric elastomer actuator (DEA) is an electrically powered soft actuator with excellent properties, which has broad application prospects in the field of soft robotics. However, the modeling and control of the DEA confront great challenges due to its complicated motion characteristics. The importance of this paper lies in proposing simple and effective dynamic modeling and motion control methods of the DEA based on the Takagi–Sugeno (T–S) fuzzy model framework and linear matrix inequality (LMI) theory, which will pave the way for the applications of soft robots actuated by DEAs. Key innovations of this paper include: (1) By cascading a square-input module and a T–S fuzzy module, a T–S fuzzy dynamic model (TSFDM) of the DEA is developed to describe its complicated motion characteristics. Since the T–S fuzzy module is composed by the fuzzy combination of a series of locally linear subsystems, the developed TSFDM of the DEA has a simple model framework, which facilitates the design of the controller and the stability proof of the whole control system. (2) The membership functions of the developed TSFDM are optimized based on the differential evolution algorithm, which facilitates to obtain a high-accuracy TSFDM. (3) Based on the developed TSFDM, a T–S fuzzy and square-root cascade (TSFSRC) controller is designed to achieve the tracking control of the DEA. In addition, the stability of the whole TSFSRC control system is proven based on the LMI theory. (4) The effectiveness of the proposed TSFSRC control approach of the DEA is experimentally verified, and the relative root-mean-square errors are less than 2.20% for all experimental results, which illustrates that the proposed approach has a strong generalization ability and satisfactory control effects from the practical application point of view.</p>