Abstract-This paper investigates the problem of fault detection for nonlinear discrete-time networked systems under an event-triggered scheme. A polynomial fuzzy fault detection filter is designed to generate a residual signal and detect faults in the system. A novel polynomial event-triggered scheme is proposed to determine the transmission of the signal. A fault detection filter is designed to guarantee that the residual system is asymptotically stable and satisfies the desired performance. Polynomial approximated membership functions obtained by Taylor series are employed for filtering analysis. Furthermore, sufficient conditions are represented in terms of sum of squares (SOS) and can be solved by SOS Tools in Matlab environment. A numerical example is provided to demonstrate the effectiveness of the proposed results.

A series of shape amphiphiles based on functionalized polyhedral oligomeric silsesquioxane (POSS) head tethered with two polymeric tails of symmetric or asymmetric compositions was designed and synthesized using sequential “grafting-from” and “click” surface functionalization. The monofunctionalization of octavinylPOSS was performed using thiol–ene chemistry to afford a dihydroxyl-functionalized POSS that was further derived into precisely defined homo- and heterobifunctional macroinitiators. Polymer tails, such as polycaprolactone and polystyrene, could then be grown from these POSS-based macroinitiators with controlled molecular weight via ring-opening polymerization and atom transfer radical polymerization (ATRP). The vinyl groups on POSS were found to be compatible with ATRP conditions. These macromolecular precursors were further modified by thiol–ene chemistry to install surface functionalities onto the POSS cage. The polymer chain composition and POSS surface chemistry can thus be tuned separately in a modular and efficient way.

We report the solution self-assembly of an ABC block terpolymer consisting of a polystyrene-block-poly(ethylene oxide) (PS-b-PEO) diblock copolymer tail tethered to a fluorinated polyhedral oligomeric silsesquioxane (FPOSS) cage in 1,4-dioxane/water. With increasing water content, abundant unconventional morphologies, including circular cylinders, two-dimensional hexagonally patterned colloidal nanosheets, and laterally patterned vesicles, are sequentially observed. The formation of toroids is dominated by two competing free energies: the end-cap energy of cylinders and the bending energy to form the circular structures. Incorporating the superhydrophobic FPOSS cages enhances the end-cap energy and promotes toroid formation. Lateral aggregation and fusion of the cylinders results in primitive nanosheets that are stabilized by the thicker rims to partially release the rim-cap energy. Rearrangement of the parallel-aligned FPOSS cylindrical cores generates hexagonally patterned nanosheets. Further increasing the water content induces the formation of vesicles with nanopatterned walls.

The self-assembly behaviors of fluorinated polyhedral oligomeric silsesquioxane (FPOSS)-based giant surfactants, consisting of an FPOSS cage and a polystyrene-block-poly(ethylene oxide) (PS-b-PEO) diblock copolymer tail, are studied in the bulk. The tethering point of the FPOSS cage on the PS-b-PEO diblock copolymer chain can be controlled precisely either at the end of the PS block or the junction point between the PS and PEO blocks, resulting in topological isomer pairs with almost identical chemical compositions but different architectures. Phase separation between the FPOSS head and the block copolymer tail creates a spatially confined environment for the PS-b-PEO component, which are uniformly end-or junction-point-immobilized on the FPOSS layer, providing a unique model system to study phase behaviors and chain conformation of tethered diblock copolymer in the condensed state. The polymer tails are highly stretched because the cross-sectional area of FPOSS head is smaller than that of the unperturbed block copolymer tail, which facilitates further phase separation between the low molecular weight PS and PEO blocks and leads to the formation of hierarchical lamellar structures among three mutually immiscible components.

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