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In this article, we present a feedback approach to the design of an attack mitigation policy for directed acyclic graph (DAG)-based distributed ledgers. We develop a model to analyze the behavior of the ledger under the so-called Tips Inflation Attack, which endangers the liveness of transactions, and we design a control strategy to counteract this attack strategy. The efficacy of this approach is showcased through a theoretical analysis, in the form of two theorems about the stability properties of the ledger with and without the controller, and extensive Monte Carlo simulations of an agent-based model of the distributed ledger.

We present order reduction results for linear time invariant descriptor systems. Results are given for both forced and unforced systems as well methods for constructing the reduced order systems. Our results establish a precise connection between classical and new results on this topic, and lead to an elementary construction of quasi-Weierstrass forms for a descriptor system. Examples are given to illustrate the usefulness of our results. [ABSTRACT FROM AUTHOR]

This article is concerned with the in-domain stabilization of a class of block diagonal infinite-dimensional systems in the presence of an uncertain and time-varying delay in the distributed control input. Two actuation schemes are considered. The first one assumes a control input that is fully distributed over the domain. The second one assumes that the control input is finite-dimensional, acting over the domain via a bounded operator. In both cases, the control design strategy consists in a predictor feedback law synthesized on a finite-dimensional truncated linear time invariant (LTI) model capturing the unstable dynamics of the original infinite-dimensional system. The predictor feedback law is designed based on the knowledge of the nominal value of the uncertain and time-varying input delay. In the second actuation scheme, the case of distinct input delays in the different scalar control input channels is considered. [ABSTRACT FROM AUTHOR]

Stability of retarded differential equations is closely related to the existence of Lyapunov–Krasovskii functionals. Even if a number of converse results have been reported regarding the existence of such functionals, there is a lack of constructive methods for their selection. For certain classes of time-delay systems for which such constructive methods are lacking, it was shown that Lyapunov–Krasovskii functionals that are also allowed to depend on the time-derivative of the state-trajectory are efficient tools for the study of the stability properties. However, in such an approach, the initial condition needs to be assumed absolutely continuous with a square integrable weak derivative. In addition, the stability results hold for initial conditions that are evaluated based on the magnitude of both the initial condition and its time-derivative. The main objective of this article is to show that, for certain classes of time-delay systems, the aforementioned stability results can actually be extended to initial conditions that are only assumed continuous and that are evaluated in uniform norm. [ABSTRACT FROM AUTHOR]

Directed acyclic graphs (DAGs) are emerging as an attractive alternative to traditional blockchain architectures for distributed ledger technology. In particular, DAG ledgers with stochastic attachment mechanisms potentially offer many advantages over blockchain, including scalability and faster transaction speeds. However, the random nature of the attachment mechanism coupled with the requirement of protection against double-spending transactions might result in an unstable system in which not all transactions get eventually validated. Such transactions are said to be orphaned, and will never be validated. Our principal contribution is to propose a simple modification to the attachment mechanism for the Tangle (the IOTA DAG architecture). This modification ensures that all transactions are validated in finite time, and preserves essential features of the popular Monte Carlo selection algorithm. In order to demonstrate these results, we derive a fluid approximation for the Tangle (in the limit of infinite arrival rate) and prove that this fluid model exhibits the desired behavior. We also present simulations that validate the results for finite arrival rates. [ABSTRACT FROM AUTHOR]

This note establishes the exponential input-to-state stability (EISS) property for a clamped-free damped string with respect to distributed and boundary disturbances. While efficient methods for establishing ISS properties for distributed parameter systems with respect to distributed disturbances have been developed during the last decades, establishing ISS properties with respect to boundary disturbances remains challenging. One of the well-known methods for well-posedness analysis of systems with boundary inputs is the use of a lifting operator for transferring the boundary disturbance to a distributed one. However, the resulting distributed disturbance involves time derivatives of the boundary perturbation. Thus, the subsequent ISS estimate depends on its amplitude, and may not be expressed in the strict form of ISS properties. To solve this problem, we show for a clamped-free damped string equation that the projection of the original system trajectories in an adequate Riesz basis can be used to establish the desired EISS property. [ABSTRACT FROM AUTHOR]

This paper addresses the robustness of the constant-delay predictor feedback in the case of distinct and uncertain time-varying input delays. Specifically, we consider the case of a predictor feedback that is designed based on the knowledge of the nominal value of the time-varying delay in each control input channel. We derive an LMI-based sufficient condition ensuring the exponential stability of the closed-loop system for small enough variations of the distinct time-varying input delays around their nominal value. Then we apply these results to the feedback stabilization of a class of diagonal infinite-dimensional boundary control systems exhibiting distinct time-varying delays in the boundary control inputs.

We consider input–output systems in descriptor form and ask when such systems can be rendered strictly positive real (SPR) via output feedback. Time- and frequency-domain conditions are given to determine when and how this is possible. In addition, a synthesis procedure for controller design is also derived. Together, the results provide a complete answer to when a linear descriptor system can be made SPR via output feedback, and provide a recipe for design of a feedback controller when one exists. [ABSTRACT FROM AUTHOR]

This paper presents a novel scan-based method for the real-time monitoring of additive manufacturing processes. Most traditional scanning techniques used for generating 3D models capture the only outer shape of the object after completion of the printing process. The method proposed in this paper differs as it relies on a layer-by-layer scanning of the 3D object directly during the printing process. This strategy has been successfully implemented with a fused filament 3D printer (PRUSA i3 MK3). Furthermore, in order to offer an increased interaction between the obtained 3D model and the user, a virtual environment has been developed for the augmented reality glasses HoloLens. The novelty of this method lies in the layer-by-layer 3D model reconstruction of both the outer shape and the inner layers of the printed part. It enables the user, directly during the printing process, to view and detect potential defects, not only at the surface but also in the inner layers of the printed object. Therefore, it can provide detailed information about the build quality and can be used as the basis of a decision-making tool.

In this paper, we present a generalization of a recent result on the almost sure consensus for networks affected by relative-state-dependent measurement noise. Specifically, we give two sufficient conditions for the synchronization of networks of diffusively coupled nonlinear nodes affected by certain state-dependent noise diffusion processes. We use this condition to study the onset of synchronization in a network of Lorenz systems and collective opinion dynamics. [ABSTRACT FROM AUTHOR]

We consider the problem of obtaining state dependent switching strategies for switching linear time-invariant systems which satisfy prespecified dwell-time constraints. Continuous-time strategies which yield exponential stability and a guaranteed level of performance are presented. We also consider discrete-time strategies in which the sampling time is independent of the dwell-times. A numerical example is included to validate the developed theory. [ABSTRACT FROM AUTHOR]

It is known that the stability of a Metzler matrix can be characterized in a Routh–Hurwitz-like fashion based on a recursive application of scalar Schur complements [1]. Our objective in this brief note is to show that recently obtained stability conditions are equivalent statements of this result and can be deduced directly therefrom using only elementary results from linear algebra. Implications of this equivalence are also discussed and several examples are given to illustrate potentially interesting system-theoretic applications of this observation. [ABSTRACT FROM AUTHOR]

The 2014 to 2016 Ebola virus disease (EVD), through the sheer size of the outbreak and combined experience within both resource-rich and resource-poor settings, allowed for more information to be gained about the clinical and pathologic features of EVD. This review highlights the range of aspects of EVD that the authors find are relevant to laboratory medicine, including the need for robust prediagnostic and laboratory processing algorithms to inform sampling of suspect patients, the vast majority of whom, in resource-rich settings, will have another diagnosis.

In recent years, a wide variety of centralised and decentralised algorithms have been proposed for residential charging of electric vehicles (EVs). In this paper, we present a mathematical framework which casts the EV charging scenarios addressed by these algorithms as optimisation problems having either temporal or instantaneous optimisation objectives with respect to the different actors in the power system. Using this framework and a realistic distribution network simulation testbed, we provide a comparative evaluation of a range of different residential EV charging strategies, highlighting in each case positive and negative characteristics.

ABSTRACTThe rapid identification of antimicrobial resistance is essential for effective treatment of highly resistant Mycobacterium tuberculosis. Whole-genome sequencing provides comprehensive data on resistance mutations and strain typing for monitoring transmission, but unlike for conventional molecular tests, this has previously been achievable only from cultures of M. tuberculosis. Here we describe a method utilizing biotinylated RNA baits designed specifically for M. tuberculosisDNA to capture full M. tuberculosisgenomes directly from infected sputum samples, allowing whole-genome sequencing without the requirement of culture. This was carried out on 24 smear-positive sputum samples, collected from the United Kingdom and Lithuania where a matched culture sample was available, and 2 samples that had failed to grow in culture. M. tuberculosissequencing data were obtained directly from all 24 smear-positive culture-positive sputa, of which 20 were of high quality (>20× depth and >90% of the genome covered). Results were compared with those of conventional molecular and culture-based methods, and high levels of concordance between phenotypical resistance and predicted resistance based on genotype were observed. High-quality sequence data were obtained from one smear-positive culture-negative case. This study demonstrated for the first time the successful and accurate sequencing of M. tuberculosisgenomes directly from uncultured sputa. Identification of known resistance mutations within a week of sample receipt offers the prospect for personalized rather than empirical treatment of drug-resistant tuberculosis, including the use of antimicrobial-sparing regimens, leading to improved outcomes.

The paper deals with the classical results of Routh and Hurwitz, Biehler and Kharitonov, concerning the stability of a linear time invariant differential equation. It is shown that these results follow directly from a Schwarz matrix representation of stable systems. [ABSTRACT FROM AUTHOR]

In this paper, we present characterisations of linear, shift-invariant, discrete-time systems that exhibit mixtures of small gain-type properties and positive real-type behaviours in a certain manner. These “mixed” systems are already fairly well characterised in the continuous-time domain, but the widespread adoption of digital controllers makes it necessary to verify whether commonly used discretisation procedures preserve the characteristic of “mixedness”. First, we analyse the effects of classical discretisation methods on the “mixed” property using Nyquist methods. A frequency domain feedback stability result is then presented. Finally, we develop a spectral-based characterisation of “mixed” discrete-time systems which provides a practical computational test that can also be applied to the MIMO case. Several examples validate the developed theory.

Electric Vehicle (EV) technology has developed rapidly in recent years, with the result that increasing levels of EV penetration are expected on electrical grids in the near future. The increasing electricity demand due to EVs is expected to provide many challenges for grid companies, and it is expected that it will be necessary to reinforce the current electrical grid infrastructure to cater for increasing loads at distribution level. However, by harnessing the power of Vehicle to Grid (V2G) technologies, groups of EVs could be harnessed to provide ancillary services to the grid. Current unbalance occurs at distribution level when currents are unbalanced between each of the phases. In this paper a distributed consensus algorithm is used to coordinate EV charging in order to minimise current unbalance. Simulation results demonstrate that the proposed algorithm is effective in rebalancing phase currents.

Recently, we showed that certain types of polyhedral Lyapunov functions for linear time-invariant systems, are preserved by diagonal Padé approximations, under the assumption that the continuous-time system matrix Ac has distinct eigenvalues. In this technical note, we show that this result also holds true in the case that Ac has non-trivial Jordan blocks. [ABSTRACT FROM AUTHOR]

Ensuring stability of switched linear systems with a guaranteed dwell time is an important problem in control systems. Several methods have been proposed in the literature to address this problem, but unfortunately they provide sufficient conditions only. This technical note proposes the use of homogeneous polynomial Lyapunov functions in the non-restrictive case where all the subsystems are Hurwitz, showing that a sufficient condition can be provided in terms of an LMI feasibility test by exploiting a key representation of polynomials. Several properties are proved for this condition, in particular that it is also necessary for a sufficiently large degree of these functions. As a result, the proposed condition provides a sequence of upper bounds of the minimum dwell time that approximate it arbitrarily well. Some examples illustrate the proposed approach. [ABSTRACT FROM PUBLISHER]

In this paper a modified Euler transformation is introduced and studied. The main merit of this transformation is to outperform stability preservation (with respect to the traditional Euler transformation) besides preserving the matrix sparseness. This is particular appealing in the analysis of positive systems since it is shown that stability is preserved independent of the sampling period. A brief collection of results for switched systems has been also provided.

This technical note has been motivated by the need to assess the preservation of polyhedral Lyapunov functions for stable continuous-time linear systems under numerical discretization of the transition matrix. This problem arises when discretizing linear systems in such a manner as to preserve a certain type of stability of the discrete time approximation. Our main contribution is to show that a continuous-time system and its Padé discretization (of any order and sampling) always share at least one common piecewise linear (polyhedral) Lyapunov function. [ABSTRACT FROM AUTHOR]

We present conditions which are necessary and sufficient for a transfer function (or transfer function matrix) to be strictly positive real. A counter-example is given to illustrate that the conditions presented here differ from those previously presented in the literature. The proof of our results differs from previous related proofs in that it only uses properties of analytic functions and matrices and does not require state-space realizations. Also, the results are not restricted to rational transfer functions with real coefficients. [ABSTRACT FROM AUTHOR]

In this note, a simple method is presented that is both necessary and sufficient for determining whether a given Metzler matrix A is Hurwitz. The method is based on the well known fact that a Hurwitz Metzler matrix is also diagonally stable. By using this fact, very simple conditions are derived for the Hurwitz stability of a Metzler matrix. The conditions are stated in terms of the signs of the diagonal entries of a sequence of lower dimensional matrices. The efficacy of the conditions is demonstrated by applying them to determine stability in several examples. [ABSTRACT FROM AUTHOR]

In this note, we consider the problem of determining necessary and sufficient conditions for the existence of a common quadratic Lyapunov function for a pair of stable linear time-invariant systems whose system matrices are of the form A, A - ghT, and where one of the matrices is singular. A necessary and sufficient condition for the existence of such a function is given in terms of the spectrum of the product A(A - ghT). The technical note also contains a spectral characterization of strictly positive real transfer functions which are strictly proper. Examples are presented to illustrate our results. [ABSTRACT FROM AUTHOR]

Necessary and sufficient conditions for Positive Realness of general transfer function matrices are derived. The conditions are 'expressed in terms of eigenvalues of matrix functions of the state matrices representation of the LTI system. Illustrative numerical examples are provided. [ABSTRACT FROM AUTHOR]

Control of large distributed cloud-based services is a challenging problem. The Distributed Rate Limiting (DRL) paradigm was recently proposed as a mechanism for tackling this problem. The heuristic nature of existing DRL solutions makes their behavior unpredictable and analytically untractable. In this paper we treat the DRL problem in a mathematical framework and propose two novel DRL algorithms that exhibit good and predictable performance. The first algorithm Cloud Control with Constant Probabilities (C3P) solves the DRL problem in best effort environments, emulating the behavior of a single best-effort queue in a fully distributed manner. The second problem we approach is the DRL in processor sharing environments. Our algorithm, Distributed Deficit Round Robin (D2R2), parameterized by parameter α, converges to a state that is, at most, O(1/α) away from the exact emulation of centralized processor sharing queue. The convergence and stability properties are fully analyzed for both C3P and D2R2. Analytical results are validated empirically through a number of representative packet level simulations. The closed-form nature of our results allows simple design rules which, together with extremely low communication overhead, makes the presented algorithms practical and easy to deploy.

In this paper, we present a probabilistic synchronization algorithm whose convergence properties are examined using tools of row-stochastic matrices. The proposed algorithm is particularly well suited for wireless sensor network applications, where connectivity is not guaranteed at all times, and energy efficiency is an important design consideration. The tradeoff between the convergence speed and the energy use is studied. [ABSTRACT FROM AUTHOR]

Abstract: Recent work on positive matrices has resulted in a new matrix method for generating chaotic maps with arbitrary piecewise constant invariant densities, sometimes known as the inverse Frobenius–Perron problem (IFPP). In this paper, we give an extensive introduction to the IFPP, describing existing methods for solving it, and we describe our new matrix approach for solving the IFPP. [Copyright &y& Elsevier]

Necessary and sufficient conditions for strict positive realness and positive realness of strictly proper functions are derived. The conditions are expressed in terms of eigenvalues of the state matrices representation of the system. Previous results rendered conditions which were significantly more complex than those for proper (but not strictly proper) functions. The present conditions for strictly proper functions are simpler than the ones for proper functions, which is consistent with intuition in this case. Illustrative numerical examples are provided. [ABSTRACT FROM AUTHOR]

In this note, we introduce the concepts of best case and worst-case convergence rates for switched linear systems. their connections to the problems of stability and stabilization are briefly discussed. For simultaneously triangularizable switched systems, explicit formulas are presented for the convergence rates in terms of the system eigenvalues. [ABSTRACT FROM AUTHOR]

In this note, we derive necessary and sufficient conditions for a single-input-single-output system to be (strictly) positive real. These conditions take the form of a spectral condition on a matrix product constructed from the state space representation of the linear time-invariant system (A, b, c, d). Numerical examples are given to Illustrate the usefulness of our conditions. [ABSTRACT FROM AUTHOR]

In this note, the problem of determining necessary and sufficient conditions for the existence of a common quadratic Lyapunov function for a pair of stable linear time-invariant systems whose system matrices A[sub 1] and A[sub 2] are in companion form is considered. It is shown that a necessary and sufficient condition for the existence of such a function is that the matrix product A[sub 1] A[sub 2] does not have an eigenvalue that is real and negative. Examples are presented to illustrate the result. [ABSTRACT FROM AUTHOR]

In this note, we define strong and weak common quadratic Lyapunov functions (CQLFs) for sets of linear time-invariant (LTI) systems. We show that the simultaneous existence of a weak CQLF of a special form, and the nonexistence of a strong CQLF, for a pair of LTI systems, is characterized by easily verifiable algebraic conditions. These conditions are found to play an important role in proving the existence of strong CQLFs for general LTI systems. [ABSTRACT FROM AUTHOR]

In this paper, necessary and sufficient conditions are derived for the existence of a common quadra‐tic Lyapunov function for a finite number of stable second order linear time‐invariant systems. Copyright © 2002 John Wiley & Sons, Ltd.

A sufficient condition for the existence of a destabilising switching sequence for the system x˙=A(t)x, A(t)∈{A1,A2,…,AM}, Ai∈IRN×N, where the Aiare Hurwitz matrices, is that there exists non-negative real constants α1,α2, ...,αм, αi≥0, ∑i=1Mαi>0, such that the matrix pencil ∑i=1MαiAihas at east one eigenvalue with a positive real part. An informal proof of this result based upon Floquet theory was presented in (Shorten, 1996; Shorten and Narendra, 1997). In this paper we present a rigourous basis for the proof of this result. Further, we use this result to identify several classes of linear switching systems, which admit the existence of a destabilising switching sequence. These systems provide insights into the relationship between the existence of a common quadratic Lyapunov function and the existence of a destabilising switching sequence for low order systems, as well as the robustness of a class of switching system that is known to be exponentially stable.

Abstract not available

ObjectiveTo determine the validity of the superstition that utterance of the word “quiet” in a clinical setting increases workload.DesignProspective randomised controlled non-inferiority study.SettingMicrobiology department of a large teaching hospital in Lancashire, UK.ParticipantsTwo members of the medical microbiology team carried out the duty work on any given week day and an on-call team member on any weekend day. 29 days were assigned in which staff were to say “Today will be a quiet day” and 32 days were assigned in which staff were to refrain from saying the word “quiet” in any context.InterventionsEach day was randomly allocated to either saying “Today will be a quiet day” (intervention group) or refraining from saying the word “quiet” (control group) in any context.Main outcome measuresThe primary outcome was mean overall workload: a composite of number of clinically related telephone calls, clinically significant results, or validated results processed by the duty medical microbiology team during a 24 hour period referred to collectively as “clinical episodes.” A difference of 30 clinical episodes was considered as the margin of non-inferiority. Secondary outcomes included the individual components of the primary outcome.ResultsWorkload was measured each day over a 61 day period (1 May to 30 June 2019). A mean 139.0 clinical episodes occurred on control days compared with 144.9 on days when the experimental intervention was uttered, a difference of 5.9 (95% confidence interval−12.9 to 24.7). The upper bound was less than the specified margin of 30, providing evidence for non-inferiority. No evidence of a difference in workload was found between interventions with any of the four components, whether considering unadjusted or adjusted analyses, or looking at the subgroups of week days or weekends.ConclusionsThe study findings refute the long held superstition that utterance of the word “quiet” impacts on clinical workload, and therefore it should not be avoided. In the era of considerable staff shortages and increased work related stress, doctors should look to other methods to increase resilience and protect their wellbeing and mental health.Trial registrationLancashire Teaching Hospitals NHS Foundation Trust’s research department SE-259.

We report a novel approach utilising a real-time PCR screening assay targeting a 53 bp tandemly repeated element present at various loci within the Mycobacterium tuberculosis (Mtb) genome. Positive samples were identified within a discriminatory melting curve range of 90–94°C, with results obtained in under one hour directly from decontaminated sputum samples without extraction. A panel of 89 smear-positive sputa were used for analytical validation of the assay with 100% concordance, with sensitivity matching that of culture. Cross reactivity was detected within a narrow range of mycobacteria other than tuberculosis (MOTT) (five sputa, three in silico), with the highest sensitivity within M. avium complex (MAC). A year-long head to head evaluation of the test with the GeneXpert platform was carried out with 104 consecutive samples at the Royal Free Hospital, UK. Receiver operating characteristics (ROC) analysis of the data revealed that the two tests are approximately equivalent in sensitivity, with the area under the curve being 0.85 and 0.80 for the GeneXpert and our assay, respectively, indicating that the test would be a cost effective screen prior to GeneXpert testing.

In this report, we describe a novel application of Baker''s map. We demonstrate that the chaotic properties of this map can be used to implement basic operations in Boolean logic. This observation leads naturally to the possibility of new computational models and implementations for conventional computational systems. Here we show that by considering the variation of the fractal dimension of its attractor, and using varying parameter values as inputs, the generalised Baker''s map can be used as a natural exclusive OR (XOR) gate. Further, this map can also be used to create other logical functions such as the AND gate. The efficacy of our results are demonstrated by means of a concrete application; namely by designing, to the best of our knowledge, for the first time, a half-adder that is constructed entirely by utilising chaotic dynamics. [Copyright &y& Elsevier]