Stability of state-delayed digital filters with overflow nonlinearities

In this work, stability of digital filters in the presence of overflow nonlinearities and time-varying delay is investigated with/without external disturbance. Two new lemmas related to characterization of overflow nonlinearities are developed. The first lemma is established with better utilization of system information which includes overflow nonlinearities, previous and current states of the digital filter. The second lemma associated with overflow nonlinearities is developed with lesser constraints. Furthermore, by utilizing the established lemmas and a new Lyapunov functional, an asymptotic stability condition is presented for the digital filter with time-varying delay and overflow nonlinearities. The developed condition is shown to be more relaxed and computationally less demanding than the existing criteria. In addition to that, a sufficient condition is derived under which the digital filter with external disturbance, overflow nonlinearities, and time-varying delay has a prescribed noise attenuation level. To show the efficacy of the proposed approach, numerical examples are presented.

A Wideband Termination Based on Laser-Scribed Lossy Microstrip Line Structures

Laser-direct writing has become an alternative method to fabricate microwave devices. We present a laser-scribed wideband open-end termination that relies on conductor loss of the microstrip line structure to obtain effective absorption. The proposed design consists of a resistive film overlapped on a strip conductor, providing an enlarged sheet-resistance range (20 Ω/□ ~ 1.2 kΩ/□) of the resistive film to reduce the fabrication difficulties. The resistive film is in tapered shape to enable small gradual changes in impedance, yielding minimized reflections (|S11|). The prototype is demonstrated utilizing the laser-direct writing technique, with a measured |S11| over −15 dB from 6 GHz to at least 30 GHz. The termination can also be used for attenuation over a −10 dB attenuation level (>8.5 GHz) with a low reflection level better than −15 dB (>2.0 GHz). This study can be employed for the applications where cheap wideband planar terminations are needed and promote fast, flexible, and low-cost prototyping or modification of the existing microwave circuits.

Ranging with Frequency Dependent Ultrasound Air Attenuation

Measuring the distance between two points has multiple uses. Position can be geometrically calculated from multiple measurements of the distance between reference points and moving sensors. Distance measurement can be done by measuring the time of flight of an ultrasonic signal traveling from an emitter to receiving sensors. However, this requires close synchronization between the emitter and the sensors. This synchronization is usually done using a radio or optical channel, which requires additional hardware and power to operate. On the other hand, for many applications of great interest, low-cost, small, and lightweight sensors with very small batteries are required. Here, an innovative technique to measure the distance between emitter and receiver by using ultrasonic signals in air is proposed. In fact, the amount of the signal attenuation in air depends on the frequency content of the signal itself. The attenuation level that the signal undergoes at different frequencies provides information on the distance between emitter and receiver without the need for any synchronization between them. A mathematical relationship here proposed allows for estimating the distance between emitter and receiver starting from the measurement of the frequency dependent attenuation along the traveled path. The level of attenuation in the air is measured online along the operation of the proposed technique. The simulations showed that the range accuracy increases with the decrease of the ultrasonic transducer diameter. In particular, with a diameter of 0.5 mm, an error of less than ± 2.7 cm (average value 1.1 cm) is reached along two plane sections of the typical room of the office considered (4 × 4 × 3 m3).

Hybrid Feedback Control for Exponential Stability and Robust H∞ Control of a Class of Uncertain Neural Network with Mixed Interval and Distributed Time-Varying Delays

This paper is concerned the problem of robust H∞ control for uncertain neural networks with mixed time-varying delays comprising different interval and distributed time-varying delays via hybrid feedback control. The interval and distributed time-varying delays are not necessary to be differentiable. The main purpose of this research is to estimate robust exponential stability of uncertain neural network with H∞ performance attenuation level γ. The key features of the approach include the introduction of a new Lyapunov–Krasovskii functional (LKF) with triple integral terms, the employment of a tighter bounding technique, some slack matrices and newly introduced convex combination condition in the calculation, improved delay-dependent sufficient conditions for the robust H∞ control with exponential stability of the system are obtained in terms of linear matrix inequalities (LMIs). The results of this paper complement the previously known ones. Finally, a numerical example is presented to show the effectiveness of the proposed methods.

Measurement-based evaluation of Google/Apple Exposure Notification API for proximity detection in a commuter bus

We report on the results of a measurement study carried out on a commuter bus in Dublin, Ireland using the Google/Apple Exposure Notification (GAEN) API. This API is likely to be widely used by Covid-19 contact tracing apps. Measurements were collected between 60 pairs of Android handset locations and are publicly available. We find that the attenuation level reported by the GAEN API need not increase with distance between handsets, consistent with there being a complex radio environment inside a bus caused by the metal-rich environment. Changing the people sitting in a pair of seats can cause variations of ±10dB in the attenuation level reported by the GAEN API. Applying the rule used by the Swiss Covid-19 contact tracing app to trigger an exposure notification to our bus measurements we find that no exposure notifications would have been triggered despite the fact that all pairs of handsets were within 2m of one another for at least 15 mins. Applying an alternative threshold-based exposure notification rule can somewhat improve performance to a detection rate of 5% when an exposure duration threshold of 15 minutes is used, increasing to 8% when the exposure duration threshold is reduced to 10 mins. Stratifying the data by distance between pairs of handsets indicates that there is only a weak dependence of detection rate on distance.

Dual-finite distributed H∞ filtering in sensor networks

Generally, distributed H∞ filtering approach achieves a certain disturbance attenuation level in the full frequency range. However, the energy of system noise or reference input usually limits in a specified frequency range. To reduce such a design conservatism, this article develops a distributed filtering approach based on dual scale, that is, filtering over a finite-time interval from time scale and also on a specified finite-frequency region from the frequency scale. Our target is to make the filtering error under sensor networks monitoring be relaxed into an ellipsoid bound rather than asymptotically converging to zero for exogenous noise in a specified frequency range. Finally, two illustrative examples demonstrate the strength of the developed filtering approach.

Ultra-wide stopband lowpass filters using ring resonators

A microstrip-based lowpass filter (LPF) containing modified ring structures has been presented. Ring resonators are used to form a sharp transition region. In addition, rectangular- and tapered-shaped suppressing cells are used to create an ultra-wide stopband region. By combining the designed ring resonator and suppressors, an LPF has been designed with −3 dB cut-off frequency at 1.83 GHz. A sharp transition region has been achieved from 1.83 (at −3 dB) to 2.1 GHz (at −60 dB). A stopband region has been concluded from 2 to 21 GHz (with the corresponding attenuation level of at least 20 dB). The measured insertion loss is better than 0.1 dB (equal to a return loss of 18.1 dB) in the passband region. The proposed circuit is fabricated and measured. The measured results have an appropriate adaption with the simulated results.

Robust H ∞ Control for the Nonlinear Cascade Systems with Passive and Nonpassive Subsystems

In this paper, H ∞ control for the uncertain switched nonlinear cascade systems with passive and nonpassive subsystems is investigated. Based on the average dwell time method, for any given passivity rate, average dwell time, and disturbance attenuation level, the feedback controllers of the subsystems by predetermined constants are designed to solve the exponential stability and L 2 -gain problems of H ∞ control for switched nonlinear cascade systems. Two examples are provided to demonstrate the effectiveness of the proposed design method.

Investigation of 2D Rainbow Metamaterials for Broadband Vibration Attenuation

Phononic crystals (PnCs) and metamaterials are widely investigated for vibration suppression owing to the bandgaps, within which, wave propagation is prohibited or the attenuation level is above requirements. The application of PnCs and metamaterials is, however, limited by the widths of bandgaps. The recently developed rainbow structures consisting of spatially varied profiles have been shown to generate wider bandgaps than periodic structures. Inspired by this design strategy, rainbow metamaterials composed of nonperiodic mass blocks in two-dimensional (2D) space were proposed in the present study. The blocks were connected by curved beams and tessellated with internal voids to adjust their masses. In order to demonstrate the effects of the rainbow design, two 2D metamaterials, with periodic and nonperiodic units, respectively, were investigated and manufactured using additive manufacturing technologies. Receptance functions, i.e., displacement frequency response functions, of the manufactured metamaterials were calculated with finite element models and measured with a testing system containing a mechanical shaker, an impedance head, and a laser Doppler vibrometer. The obtained numerical and experimental results showed that the metamaterial with rainbow blocks has extended bandgaps compared with the periodic metamaterial.