Stability margins for multilinear interval systems by way of phase conditions: A unified approach

A simple way of checking the stability with respect to an arbitrary stability region of a family of polynomials containing a vector of parameters varying within prescribed intervals is discussed. It is assumed that the parameters appear affine multilinearly in the characteristic polynomial coefficients. The condition proposed is simply to check the phase difference of the vertex polynomials. This test based on the mapping theorem significantly reduces computational complexity. Mathematical proofs are omitted. The results can be used to determine various stability margins of control systems containing interconnected interval subsystems. These include the gain, phase, time-delay, H(sup infinity), and nonlinear sector bounded stability margins of multilinear interval systems

Parametric stability margin for multilinear interval control systems

Recently, a necessary and sufficient condition to determine the robust stability of a multilinear interval control system has been reported as an extension of the well-known Box theorem which deals with the linear affine case. A simple but computationally efficient algorithm, based on the above result, to check the robust stability of such systems is introduced. The method is also extended to find the parametric stability margin of such a system

The 32nd CDC: Robust stabilizer synthesis for interval plants using Nevanlina-pick theory

The synthesis of robustly stabilizing compensators for interval plants, i.e., plants whose parameters vary within prescribed ranges is discussed. Well-known H(sup infinity) methods are used to establish robust stabilizability conditions for a family of plants and also to synthesize controllers that would stabilize the whole family. Though conservative, these methods give a very simple way to come up with a family of robust stabilizers for an interval plant

Parametric Robust Control and System Identification: Unified Approach

During the period of this support, a new control system design and analysis method has been studied. This approach deals with control systems containing uncertainties that are represented in terms of its transfer function parameters. Such a representation of the control system is common and many physical parameter variations fall into this type of uncertainty. Techniques developed here are capable of providing nonconservative analysis of such control systems with parameter variations. We have also developed techniques to deal with control systems when their state space representations are given rather than transfer functions. In this case, the plant parameters will appear as entries of state space matrices. Finally, a system modeling technique to construct such systems from the raw input - output frequency domain data has been developed

Recent Developments in Smart Adaptive Structures for Solar Sailcraft

The "Smart Adaptive Structures for Solar Sailcraft" development activity at MSFC has investigated issues associated with understanding how to model and scale the subsystem and multi-body system dynamics of a gossamer solar sailcraft with the objective of designing sailcraft attitude control systems. This research and development activity addressed three key tasks that leveraged existing facilities and core competencies of MSFC to investigate dynamics and control issues of solar sails. Key aspects of this effort included modeling and testing of a 30 m deployable boom; modeling of the multi-body system dynamics of a gossamer sailcraft; investigation of control-structures interaction for gossamer sailcraft; and development and experimental demonstration of adaptive control technologies to mitigate control-structures interaction

Concerning the Wave equation on Asymptotically Euclidean Manifolds

We obtain KSS, Strichartz and certain weighted Strichartz estimate for the wave equation on $(\R^d, \mathfrak{g})$, $d \geq 3$, when metric $\mathfrak{g}$ is non-trapping and approaches the Euclidean metric like $x ^{- \rho}$ with $\rho>0$. Using the KSS estimate, we prove almost global existence for quadratically semilinear wave equations with small initial data for $\rho> 1$ and $d=3$. Also, we establish the Strauss conjecture when the metric is radial with $\rho>0$ for $d= 3$.Comment: Final version. To appear in Journal d'Analyse Mathematiqu

Evaluating the Patient-Reported Outcomes Measurement Information System scales in acute intermittent porphyria.

PurposeAcute intermittent porphyria (AIP) is a rare inborn error of heme biosynthesis characterized by life-threatening acute attacks. Few studies have assessed quality of life (QoL) in AIP and those that have had small sample sizes and used tools that may not have captured important domains.MethodsBaseline data from the Porphyrias Consortium's Longitudinal Study were obtained for 259 patients, including detailed disease and medical history data, and the following Patient-Reported Outcomes Measurement Information System (PROMIS) scales: anxiety, depression, pain interference, fatigue, sleep disturbance, physical function, and satisfaction with social roles. Relationships between PROMIS scores and clinical and biochemical AIP features were explored.ResultsPROMIS scores were significantly worse than the general population across all domains, except depression. Each domain discriminated well between asymptomatic and symptomatic patients with symptomatic patients having worse scores. Many important clinical variables like symptom frequency were significantly associated with domain scores in univariate analyses, showing responsiveness of the scales, specifically pain interference and fatigue. However, most regression models only explained ~20% of the variability observed in domain scores.ConclusionPain interference and fatigue were the most responsive scales in measuring QoL in this AIP cohort. Future studies should assess whether these scales capture longitudinal disease progression and treatment response

Influence of major mergers on the radio emission of elliptical galaxies

We investigate the influence of major mergers on the radio emission of elliptical galaxies. We use a complete sample of close pairs, which contains 475 merging and 1828 non-merging paired elliptical galaxies of M_r<-21.5 selected from the Sloan Digital Sky Survey. In addition, a control sample of 2000 isolated field galaxies is used for comparison. We cross-identify the optical galaxies with the radio surveys of FIRST and NVSS. We find that the radio fraction of merging paired galaxies is about 6%, which is slightly higher than the 5% obtained for non-merging paired galaxies, although these values are consistent with each other owing to the large uncertainty caused by the limited sample. The radio fraction is twice as that of isolated galaxies, which is less than 3%. Radio emission of elliptical galaxies is only slightly affected by major mergers, but predominantly depends on their optical luminosities. Therefore, merging is not important in triggering the radio emission of elliptical galaxies.Comment: 5 pages, 5 figures, 1 table, accepted for publication in A&A, minor change

Thermal Emission as a Test for Hidden Nuclei in Nearby Radio Galaxies

The clear sign of a hidden quasar inside a radio galaxy is the appearance of quasar spectral features in its polarized (scattered) light. However that observational test requires suitably placed scattering material to act as a mirror, allowing us to see the nuclear light. A rather robust and more general test for a hidden quasar is to look for the predicted high mid-IR luminosity from the nuclear obscuring matter. The nuclear waste heat is detected and well isolated in the nearest narrow line radio galaxy, Cen A. This confirms other indications that Cen A does contain a modest quasar-like nucleus. However we show here that M87 does not: at high spatial resolution, the mid-IR nucleus is seen to be very weak, and consistent with simple synchrotron emission from the base of the radio jet. This fairly robustly establishes that there are "real" narrow line radio galaxies, without the putative accretion power, and with essentially all the luminosity in kinetic form. Next we show the intriguing mid-IR morphology of Cygnus A, reported previously by us and later discussed in detail by Radomski et al. (2002). All of this mid-IR emission is consistent with reprocessing by a hidden quasar, known to exist from spectropolarimetry by Ogle et al. (1997) and other evidence.Comment: 21 pages, 5 figure