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In this paper, we explore the geometric structures of the H∞ central controllers for descriptor systems based on the notions of deflating subspaces for singular matrix pencil. A reduced order H∞ controller is given based on the geometric structures addressed in this paper. The geometric connection between the plant and the H∞ controllers is then studied. A numerical example is provided. In terms of the notions of deflating subspaces, all the results and proofs given are clear and simple.

Indium tin oxide (ITO; Indium oxide with tin doping) nanowires were first prepared via the electrochemical deposition and an oxidization method based on an AAO template. FE-SEM results show the synthesized ITO nanowires to have an approximate length of 8–10 μm with an aspect ratio close to 167. ITO nanowires with an In/Sn weight ratio of 8.8 (∼9:1) were observed from EDS. The crystal structure of ITO nanowires showed that all the peaks within the spectra can be indexed to In2O3 with a cubic structure. The ITO nanowire is single-crystalline determined from selected area electron diffraction (SAED) patterns. An optical energy gap (Eg) of the ITO nanowire is 3.8 eV.

In this study, one-dimensional (1D) indium zinc oxide (IZO; Indium oxide with heavy zinc doping of 30 at %) nanowires was synthesized via electrodeposition and an oxidization method with porous anodic alumina membrane (AAM), which had an average diameter of about 60 nm. As FE-SEM results showed the synthesized IZO nanowires had an approximate length of 6–8 μm with a high aspect ratio of about 116. IZO nanowires with an Zn/(In + Zn) atomic ratio of 0.301 (∼0.3) were observed from EDS. XRD and SAED analyses show the synthesized nanowires were of single-crystal cubic structure. The UV/Visible/NIR absorption of the IZO nanowires showed an absorption peak of around 330 nm with a direct band gap energy ( E g ) of 3.5 eV.

In this paper, the geometric structure of observer-based controllers is investigated in order to characterize the controllable and unobservable subspaces of the H"2 optimal and the H"~ central controllers. It is shown that the controllable and unobservable subspaces of the H"2 optimal and the H"~ central controllers can be characterized by the kernel and image subspaces of the solutions of two Lyapunov equations. Under this characterization, the connection between the geometric subspaces and the dynamic behavior of the plant and those of the H"2 optimal and H"~ controllers is derived. It is also shown that the H"2 optimal and the H"~ central controllers inherit a certain part of the given plant dynamics in the geometric sense. A numerical example is also given for illustration.

Crystalline CuS nanowire arrays have been successfully fabricated by an AC with DC electrodeposition from aqueous solutions of dimethylsulfoxide solution containing copper chloride and elemental sulfur into oxalic anodic alumina membranes (AAM). The results of X-ray diffraction show that the as-synthesized nanowires are crystalline with highly preferential [100] orientation and show the hexagonal structure. Scanning electron microscopy indicates that the ordered CuS nanowire arrays are completely embedded into AAM. These nanowires have uniform diameters of approximately 60 nm, and their lengths are up to tens of micrometers. The absorbance in UV–Vis spectrum might be attributed from the varied copper sulfide phase. The high energy absorbance might be due to the characteristic of Cu 2 S composition of the few amounts in our sample. The broad and strong absorbance in the near-IR region might be due to the characteristic of CuS.

Under some rank condition, a new version of bounded real lemma, which is expressed in terms of an admissible solution of a generalized discrete-time algebraic Riccati equation (GDARE) rather than inequality, is presented for linear discrete-time descriptor systems. When a linear discrete-time descriptor system is admissible, with the H∞-norm of its transfer matrix less than a prescribed positive number γ, a constructive procedure is also given to obtain an admissible solution of the above-mentioned GDARE.

In this letter, we successfully synthesize CuxS nanowires by sulfuring the copper nanowires at varied temperatures. When the annealing temperatures reach 400, 450, and 500 °C, the x values are equal to 1.03, 1.26, and 1.43, respectively. The CuxS nanowire arrays are highly ordered and have high wire packing densities. At 400 °C sulfured temperature, the CuS nanowire phase with a strongly preferential peak [110] indicates that the nanowire arrays should point to the [110] direction. The UV–vis spectroscopy measurement shows only one broad absorption peak that appears at 802 nm in near-IR region. This proves that the sulfured nanowire has pure CuS phase.

PbS nanowires with 30 nm and 60 nm diameter fabricated under the same condition of electrochemical deposition with sulfuric and oxalic anodic alumina membranes (AAM), respectively, have been successfully prepared in order to study their optical properties in relation to their size. Scanning electron microscopy indicates that the 60 nm PbS nanowire arrays have the same shape with the 30 nm. X-ray diffraction result shows that 60 nm PbS nanowires are crystalline and have a highly (200) preferential orientation like 30 nm ones. UV spectrum considers the nanowire size decrease as the absorption peak shifts to the blue. The quantum confinement effects compared between 30 nm and 60 nm PbS nanowire arrays were observed by the measurements of ultraviolet–visible absorption spectroscopy (UV–vis).