In this article, we address the problem of singular value decomposition of polynomial matrices and eigenvalue decomposition of para-Hermitian matrices. Discrete Fourier transform enables us to propose a new algorithm based on uniform sampling of polynomial matrices in frequency domain. This formulation of polynomial matrix decomposition allows for controlling spectral properties of the decomposition. We set up a nonlinear quadratic minimization for phase alignment of decomposition at each frequency sample, which leads to a compact order approximation of decomposed matrices. Compact order approximation of decomposed matrices makes it suitable in filterbank and multiple-input multiple-output (MIMO) precoding applications or any application dealing with realization of polynomial matrices as transfer function of MIMO systems. Numerical examples demonstrate the versatility of the proposed algorithm provided by relaxation of paraunitary constraint, and its configurability to select different properties.

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Aromatic polymers, such as sulfonated poly(2,6-dimethyl-1,4-phenylene oxide) (SPPO), sulfonated poly(ether ether ketone) (SPEEK), and sulfonated poly(ether sulfone) (SPES), at the optimum degrees of sulfonation (DS), are suggested and evaluated as alternatives to Nafion for direct methanol fuel cells (DMFCs) applications. To reduce the methanol cross-over, which decreases the efficiency of the cell, organically modified montmorillonite nanoclays (OMMT) were added at 1 wt% to the sulfonated matrices with the optimum DS. The X-ray diffraction (XRD) patterns of nanocomposite membranes proved that the nanoclay layers were exfoliated. The proton conductivity and methanol permeability of the membranes, as well as the ion-exchange capacity (IEC), were measured. The selectivity parameter, ratio of proton conductivity to methanol permeability, was identified at 25 • C for the nanocomposite membranes and the results were compared with Nafion117. Finally, the DMFC performance tests were investigated at 70 • C and 5 M methanol feed for the manufactured nanocomposite polyelectrolyte membranes (PEMs). The SPEEK-based nanocomposite membrane showed the highest maximum power density in comparison with Nafion 117 and SPES and SPPO nanocomposite membranes. The results indicated that the nanocomposite membranes were promising PEMs for DMFC applications.

The preparation and characterization of the nanocomposite polyelectrolyte membranes, based on Nafion, sulfonated multi‐walled carbon nanotubes (MWCNT‐SO3H) and imidazole modified multi‐walled carbon nanotubes (MWCNT‐Im), for direct methanol fuel cell applications is described. The results showed that the modification of multi‐walled carbon nanotubes (MWCNT) with proton‐conducting groups (sulfonic acid groups or imidazole groups) could enhance the proton conductivity of the nanocomposite membranes in comparison to Nafion 117. Regarding the interactions between the protonated imidazole groups, grafted on the surface of MWCNT, and the negatively charged sulfonic acid groups of Nafion, new electrostatic interactions can be formed in the interface of the Nafion and MWCNT‐Im, which result in both lower methanol permeability and higher proton conductivity. The physical characteristics of these manufactured nanocomposite membranes were investigated by thermogravimetric analysis, differential scanning calorimetry, Fourier transform infrared spectroscopy, water uptake, methanol permeability, and ion exchange capacity, as well as proton conductivity. The Nafion/MWCNT‐Im membranes showed the higher proton conductivity, lower methanol permeability, and, as a consequence, a higher selectivity parameter in comparison to the neat Nafion or Nafion membrane containing MWCNT‐SO3H or ─OH functionalized multi‐walled carbon nanotubes (MWCNT‐OH) membranes. The obtained results indicated that the Nafion/MWCNT‐Im membranes could be used as efficient polyelectrolyte membranes for direct methanol fuel cell applications.