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Processing signals from open-loop system realizations can replace real-time operation using actuators in the design of closed-loop eigenstructures. One merit of the signal processing-based implementation is that it, in principle, allows virtual compensators of user-defined model order since the closed-loop systems are not to be realized during physical testing. The present paper explores the implication of the virtual compensator order in terms of the Fisher information on unknown parameters to be estimated in a model updating context. A numerical example with a structural system of engineering interest is presented that demonstrates the basic points outlined in the paper. 

Context. Models of stellar structure and evolution can be constrained using accurate measurements of the parameters of eclipsing binary members of open clusters. Multiple binary stars provide the means to tighten the constraints and, in turn, to improve the precision and accuracy of the age estimate of the host cluster. In the previous two papers of this series, we have demonstrated the use of measurements of multiple eclipsing binaries in the old open cluster NGC 6791 to set tighter constraints on the properties of stellar models than was previously possible, thereby improving both the accuracy and precision of the cluster age. Aims. We identify and measure the properties of a non-eclipsing cluster member, V56, in NGC 6791 and demonstrate how this provides additional model constraints that support and strengthen our previous findings. Methods. We analyse multi-epoch spectra of V56 from FLAMES in conjunction with the existing photometry and measurements of eclipsing binaries in NGC6971. Results. The parameters of the V56 components are found to be M p  = 1.103 ± 0.008  M ⊙ and M s  = 0.974 ± 0.007  M ⊙ , R p  = 1.764 ± 0.099  R ⊙ and R s  = 1.045 ± 0.057  R ⊙ , T eff,p  = 5447 ± 125 K and T eff,s  = 5552 ± 125 K, and surface [Fe/H] = +0.29 ± 0.06 assuming that they have the same abundance. Conclusions. The derived properties strengthen our previous best estimate of the cluster age of 8.3 ± 0.3 Gyr and the mass of stars on the lower red giant branch (RGB), which is M RGB  = 1.15 ± 0.02  M ⊙ for NGC 6791. These numbers therefore continue to serve as verification points for other methods of age and mass measures, such as asteroseismology. 

Abstract We report the observation of gravitational waves from two binary black hole coalescences during the fourth observing run of the LIGO–Virgo–KAGRA detector network, GW241011 and GW241110. The sources of these two signals are characterized by rapid and precisely measured primary spins, nonnegligible spin–orbit misalignment, and unequal mass ratios between their constituent black holes. These properties are characteristic of binaries in which the more massive object was itself formed from a previous binary black hole merger and suggest that the sources of GW241011 and GW241110 may have formed in dense stellar environments in which repeated mergers can take place. As the third-loudest gravitational-wave event published to date, with a median network signal-to-noise ratio of 36.0, GW241011 furthermore yields stringent constraints on the Kerr nature of black holes, the multipolar structure of gravitational-wave generation, and the existence of ultralight bosons within the mass range 10⁻¹³–10⁻¹²eV. 

Abstract On 2023 November 23, the two LIGO observatories both detected GW231123, a gravitational-wave signal consistent with the merger of two black holes with masses $137_{-18}^{+23}{M}_{\odot }$and $101_{-50}^{+22}{M}_{\odot }$(90% credible intervals), at a luminosity distance of 0.7–4.1 Gpc, a redshift of $0.40_{-0.25}^{+0.27}$, and with a network signal-to-noise ratio of ∼20.7. Both black holes exhibit high spins— $0.90_{-0.19}^{+0.10}$and $0.80_{-0.52}^{+0.20}$, respectively. A massive black hole remnant is supported by an independent ringdown analysis. Some properties of GW231123 are subject to large systematic uncertainties, as indicated by differences in the inferred parameters between signal models. The primary black hole lies within or above the theorized mass gap where black holes between 60–130M_⊙should be rare, due to pair-instability mechanisms, while the secondary spans the gap. The observation of GW231123 therefore suggests the formation of black holes from channels beyond standard stellar collapse and that intermediate-mass black holes of mass ∼200M_⊙form through gravitational-wave-driven mergers. 

The gravitational-wave signal GW250114 was observed by the two LIGO detectors with a network matched-filter signal-to-noise ratio of 80. The signal was emitted by the coalescence of two black holes with near-equal masses $m_1={33.6}_{-0.8}^{+1.2}{M}_{\odot }$and $m_2={32.2}_{-1.3}^{+0.8}{M}_{\odot }$, and small spins ${\chi }_{1,2}\le 0.26$(90% credibility) and negligible eccentricity $e\le 0.03$. Postmerger data excluding the peak region are consistent with the dominant quadrupolar $(\ell =|m|=2)$mode of a Kerr black hole and its first overtone. We constrain the modes’ frequencies to $\pm 30\%$of the Kerr spectrum, providing a test of the remnant’s Kerr nature. We also examine Hawking’s area law, also known as the second law of black hole mechanics, which states that the total area of the black hole event horizons cannot decrease with time. A range of analyses that exclude up to five of the strongest merger cycles confirm that the remnant area is larger than the sum of the initial areas to high credibility.