## 1 Introduction  
Soft robots have been used in a wide range of applications. Considerable growth in the application area is expected in the coming years [1; 2]. The growing interest in soft robots comes from the good performance of these materials in environments which is not best suited for conventional rigid bodies. Soft robots utilize the compliance, adaptability, and flexibility of soft materials and actuation methods to develop highly adaptive structures [3]. Soft robots are mainly composed of materials with low Young's modulus (around 1 GPa). Typical materials to which this applies are silicone, rubber, or other elastomeric polymers. The strength and stiffness of these soft materials can be improved by adding reinforcement materials such as fibers. The resulting combination called textile reinforced composites is lightweight, strong, and resistant that makes it ideal for diverse soft robotics applications [4; 5]. Engineering applications of these composites exist in robotics, aerospace, automotive, underwater vehicles, and other areas [6]. The elastic properties of textile reinforced composites require smart actuators which possess adaptability and deformability. Smart materials which include piezoelectric materials, shape memory alloys (SMA), and dielectric elastomers have been used in diverse flexible structures [7; 8; 9]. Among these smart materials, SMAs have the advantages of simple structure, small size, excellent (i.e., higher) force to weight ratio, large displacement, and high stiffness [10; 11]. SMAs are capable of returning to a predefined shape when heated. This phenomenon is called the _shape memory effect_ (SME) and is due to crystalline phase transformation from martensite (low temperature phase) to austenite (high temperature phase) [12]. This transformation gives rise to a hysteresis effect which is highly nonlinear. While contracted upon heating, the SMAs exerts a force which is used for actuation. One of the efficient methods for heating the SMAs is resistive heating from an electrical current. Through this method, the deflection and retraction of the wire can be made controllable. The performance of a shape memory actuator depends significantly on the accuracy of its controls, which is in turn dependent on the SMAs mathematical model. Among the different modeling approaches available in the literature, phenomenological or macro approaches are more suitable to be used for engineering applications. This includes constitutive models like the Tanaka model [13], the Liang and [PERSON] model [14], the Brinson model [15], and the hysteresis models such as the Preisach model [16], the Krasnosel'skii-Pokrovskii model [17], and the Prandtl-Ishlinskii model [18]. However, due to the complicated dynamics of the hysteresis effect in SMAs, these models are mainly complex and difficult to use for designing a suitable controller. Furthermore, not only the modeling of the involved SMA actuators is required, but of the structure of the entire system as well. One alternative for obtaining the mathematical model of the system is using experimental modeling or system identification to derive simpler equations [19; 20]. The nonlinear relationship between the inputs and outputs of the system can be then represented by a linear transfer function which includes the nonlinearities of the system as unstructured uncertainty. The purpose of this paper is to use the unstructured uncertainty approach for modeling a textile-reinforced composite system actuated by shape memory alloys. The paper extends preliminary findings presented in the conference paper [21]. Different uncertainty models are introduced, applied to the system and consequently compared. Based on the robust stability analysis a proportional-integral controller is then designed to verify the effectiveness of this approach. The objective of the controller is to stabilize the position of the system for a fixed reference. The performance of this controller is compared with a classical one. The rest of the paper is organized as follows.