Robust stability of diamond families of polynomials with complex coefficients

Like the interval model of Kharitonov, the diamond model proves to be an alternative powerful device for taking into account the variation of parameters in prescribed ranges. The robust stability of some kinds of diamond polynomial families with complex coefficients are discussed. By exploiting the geometric characterizations of their value sets, we show that, for the family of polynomials with complex coefficients and both their real and imaginary parts lying in a diamond, the stability of eight specially selected extreme point polynomials is necessary as well as sufficient for the stability of the whole family. For the so-called simplex family of polynomials, four extreme point and four exposed edge polynomials of this family need to be checked for the stability of the entire family. The relations between the stability of various diamonds are also discussed

Exploiting structure: Introduction and motivation

This annual report summarizes the research activities that were performed from 26 Jun. 1993 to 28 Feb. 1994. We continued to investigate the Robust Stability of Systems where transfer functions or characteristic polynomials are affine multilinear functions of parameters. An approach that differs from 'Stability by Linear Process' and that reduces the computational burden of checking the robust stability of the system with multilinear uncertainty was found for low order, 2-order, and 3-order cases. We proved a crucial theorem, the so-called Face Theorem. Previously, we have proven Kharitonov's Vertex Theorem and the Edge Theorem by Bartlett. The detail of this proof is contained in the Appendix. This Theorem provides a tool to describe the boundary of the image of the affine multilinear function. For SPR design, we have developed some new results. The third objective for this period is to design a controller for IHM by the H-infinity optimization technique. The details are presented in the Appendix

Exploiting structure: Introduction and motivation

Research activities performed during the period of 29 June 1993 through 31 Aug. 1993 are summarized. The Robust Stability of Systems where transfer function or characteristic polynomial are multilinear affine functions of parameters of interest in two directions, Algorithmic and Theoretical, was developed. In the algorithmic direction, a new approach that reduces the computational burden of checking the robust stability of the system with multilinear uncertainty is found. This technique is called 'Stability by linear process.' In fact, the 'Stability by linear process' described gives an algorithm. In analysis, we obtained a robustness criterion for the family of polynomials with coefficients of multilinear affine function in the coefficient space and obtained the result for the robust stability of diamond families of polynomials with complex coefficients also. We obtained the limited results for SPR design and we provide a framework for solving ACS. Finally, copies of the outline of our results are provided in the appendix. Also, there is an administration issue in the appendix

The H(sub infinity) optimal controller design and reduction for the inertial hold mode of the attitude control system of the XTE spacecraft

The Inertial Hold Mode (IHM) is one mode of the attitude control system of the X-ray Timing Explorer spacecraft that is disturbed by both parametric uncertainties and external torque disturbance. The IHM model is modified into a typical H-infinity mixed-sensitivity problem through choosing suitable weighting functions W(sub 1)(s) and W(sub 3)(s). The controller is designed by the H-infinity optimization technique with the transformation of shifting the imaginary axis. It can stabilize the plant with uncertainties from the natural frequencies of the flexible body. The gain margin and phase margin of the system are 24.03 db and 55.04 deg, respectively. The step response attenuates to zero within 150 seconds. These show that the controller satisfies the specified requirements. Since the order of the controller appears high, it is reduced to fourth order one. The results show that the stability and the performance of the system with the reduced controller are retained perfectly

Role of CTSC in Glioblastoma Based on Oncomine and TCGA Database

Background and objective Glioblastoma (GBM) is one of the malignant tumors causing death worldwide. Most patients were found in the middle and late stages and had poor prognosis. The purpose of this study was to investigate the expression and significance of CTSC in GBM. Methods The information about CTSC in Oncomine database was collected and analyzed twice. The role of CTSC in GBM was meta-analyzed. The expression of CTSC in glioma cell lines was retrieved by CCLE database, and the survival of patients was analyzed by TCGA database. Results A total of 1,459 different types of CTSC were collected in Oncomine database, 134 of which had statistical differences in CTSC expression, 89 of which had increased CTSC expression and 45 of which had decreased CTSC expression. A total of 50 studies involving the expression of CTSC in GBM cancer and normal tissues included 1,189 samples. Compared with the control group, CTSC was highly expressed in GBM (P < 0.05). Moreover, CTSC was highly expressed in glioma cell lines. There was a correlation between the expression of CTSC and the overall survival rate of GBM. The overall survival rate of patients with high expression of CTSC was worse, while the prognosis of patients with low expression of SPC24 was better (P < 0.05). Conclusion Through the in-depth mining of oncomine gene chip database, we propose that CTSC is highly expressed in GBM tissues and is related to the prognosis of GBM, which may provide an important theoretical basis for the treatment of glioma