This paper investigates the issue of sliding mode observer (SMO) design for T-S fuzzy descriptor fractional order systems (FOSs) with fractional order 0 < $\alpha$ < 1. Firstly, a fractional order integral-type sliding surface function in the form of T-S fuzzy model is constructed. By converting the integraltype sliding surface function, the assumption that all local input matrices are identical, which is involved in most existing results about sliding mode control (SMC) for T-S fuzzy systems, can be removed. Then, a new sufficient condition is proposed in terms of linear matrix inequalities (LMIs) which guarantees the admissibility of the sliding mode dynamics and obtains appropriate solutions of the SMO gain matrix Li. Moreover, adaptive SMC strategy is adopted such that the reachability condition and state feedback control can be ensured. Finally, three numerical examples are given to verify the effectiveness of our results.

This paper deals with the H∞ adaptive sliding mode fault tolerant control problem for uncertain Takagi-Sugeno (T-S) fuzzy fractional order systems (FOSs) of fractional order 0<α<1 with mismatched disturbances. Adaptive laws are designed to estimate the upper bounds of the nonlinear terms. A sliding surface with reduced dimension is constructed by the method of state transformation. A sufficient condition in terms of linear matrix inequalities (LMIs) is established which guarantees the stability of the sliding motion. Then, a new control law is designed to make the resulting control system reach the sliding surface in a finite time. Both state and output feedback control forms are addressed. The proposed methods are illustrated by numerical simulations.

In this paper, an infrared (IR) and visible (VIS) image fusion algorithm is designed for the injection of the IR objects into the VIS background in a perceptual manner. It consists of four parts: image decomposition, layer fusion, image reconstruction, and image refinement. An edge-preserving filter is constructed for image decomposition, in which an $L_1$ regularization term and a fractional gradient are newly introduced. The resulting filter is capable of not only preserving edges, but also attenuating the influence of the IR background. A two-layer fusion rule is adopted, which consists of a routine weighted-average fusion rule and an injected fusion rule. It ensures that the fused image is with both rich background information of the VIS image and the salient features of the IR image. After image reconstruction, the guided filter is applied again to the IR image to refine the fused image, such that the final version of the fused image is with satisfactory human visual perception under even dim lights. The effectiveness and superiority of our fusion algorithm are illustrated by the results of ablation studies and comparative experiments.

In the paper, an image enhancement algorithm based on a rough set and fractional order differentiator is proposed. By combining the rough set theory with a Gaussian mixture model, a new image segmentation algorithm with higher immunity is obtained. This image segmentation algorithm can obtain more image layers with concentrating information and preserve more image details than traditional algorithms. After preprocessing, the segmentation layers will be enhanced by a new adaptive fractional order differential mask in the Fourier domain. Experimental results and numerical analysis have verified the effectiveness of the proposed algorithm.