Stability Of Such Systems Research Articles

Exact bounds for robust stability of output feedback controlled fractional‐order systems with single parameter perturbations

SummaryThis article investigates exact robust stability bounds of output feedback controlled fractional‐order systems with the commensurate order and single parameter perturbations in all system coefficient matrices. First, a sufficient and necessary condition for robust asymptotical stability of such systems is obtained by using the Kronecker product. Then the maximal upper bounds and minimum lower bounds for robust asymptotical stability are established, respectively, without conservatism by transforming such problems into checking whether the matrix with single parameter perturbations is nonsingular or not. Finally, two numerical examples are given to show the effectiveness of the proposed results.

Averaging of linear systems with almost periodic coefficients: A time-delay approach

We study stability of linear systems with fast almost periodic coefficients that are piecewise-continuous in time. The classical averaging method guarantees the stability of such systems for small enough values of parameter provided the corresponding averaged system is stable. However, it is difficult to find an upper bound on the small parameter by using classical tools for asymptotic analysis. In this paper we introduce an efficient constructive method for finding an upper bound on the value of the small parameter that guarantees a desired exponential decay rate. We transform the system into a model with time-delays of the length of the small parameter. The resulting time-delay system is a perturbation of the averaged system. The averaged system is supposed to be exponentially stable. The stability of the time-delay system guarantees the stability of the original one. We construct an appropriate Lyapunov functional for finding sufficient stability conditions in the form of linear matrix inequalities (LMIs). The upper bound on the small parameter that preserves the exponential stability is found from the LMIs. Two numerical examples (stabilization by vibrational control and by time-dependent switching) illustrate the efficiency of the method. Moreover, we apply the time-delay approach to persistently excited systems that leads to a novel quadratic time-independent Lyapunov functional for such systems. We further extend our method to input-to-state stability (ISS) analysis. Finally the results are extended to linear fast-varying systems with time-varying delays.

Metodika kompleksnoy otsenki ustoychivosti beregovykh eko-sotsio-ekonomicheskikh sistem na osnove indikatornogo podkhoda

Currently, there is no unified approach to determining the assessment of stability of coastal eco-socio-economic systems as separate objects of study and forecasting their state caused by influence of various factors. The paper proposes a methodology for comprehensive assessment of stability of such systems in tasks of spatial planning and socioeconomic development of a maritime complex based on an indicator approach. The main novelty is the use of a combination of analytical, indicator and geoinformation methods based on the analysis of statistical information. The result is a unified and quantitative methodology of multifactor sustainability assessment of coastal eco-socio-economic systems, which gives the opportunity not only to analyze numerical estimates of sustainability, but also to evaluate and analyze trends of the system. It is proposed to use a comprehensive indicator system consisting of five factor subsystems: general economic, sociodemographic, resource-industrial, nature-environmental and political-geographical. Due to the indicator approach and methodology of using statistical parameters, it is possible to obtain quantitative estimates both for individual parameters and factors and their entirety in the form of a comprehensive integral indicator of stability of the coastal eco-socio-economic system. This method can be used at regional and district spatial levels, which will allow for a factor-by-factor analysis of stability of a coastal eco-socio-economic system, spatial analysis of various coastal systems of the same spatial level (region, district, local municipality, etc.), as well as temporal analysis with identification of trends in variability. Implementation of the method in a form of GIS “Coastal eco-socio-economic system” will allow for spatial planning and forecast for sustainable development, taking into account medium- and longterm environmental and socio-economic changes and increase the efficiency of a decisionmaking process in development of coastal eco-socio-economic systems

A nonlinear observer-based adaptive robust control approach for a class of uncertain asymmetric hysteretic systems

This article presents a robust control scheme for a class of asymmetric hysteretic systems with both parametric uncertainties and external disturbances, where an asymmetric Bouc–Wen model is adopted to represent the hysteretic behavior. A novel adaptive non-singular terminal sliding mode control methodology with hysteretic state estimation is proposed to achieve finite-time stabilization of such systems for vibration suppressions. In the proposed control framework, a hysteresis observer is constructed to capture the unmeasurable hysteretic force, and the adaptive control technique is used to accommodate the hysteretic uncertainties and unknown system parameters. Moreover, a fast terminal sliding mode controller without the singularity problem is designed to improve the robustness and dynamic performance of such systems, where the terminal sliding mode function is proposed to guarantee the finite-time convergence of the system states, and the reaching law with fractional power is constructed to accelerate the occurrence of the corresponding terminal sliding mode surface. Meanwhile, the finite-time stability of the whole closed-loop system is also analyzed. Finally, numerical simulation results deployed on a magnetorheological elastomer vibration isolation system are provided to validate the effectiveness of the proposed control algorithm.

Extensions of Razumikhin-type stability theorems for nonlinear time-delay systems on time scales

This paper focuses on the stability analysis of nonlinear time-delay systems on time scales, which are of generality as they can include not only the traditional continuous and discrete ones, but also some other cases, such as systems on general uniform or non-uniform time domains. One existing classical method for analyzing stability of such systems is the Razumikhin-type theorem with requiring the time derivative of relating Lyapunov function to be non-positive for uniform stability and negative for uniform asymptotic or exponential stability, which are difficult to be satisfied. To relax these restrictions, by introducing the time-scale type uniformly stable function and uniformly asymptotically stable function, this paper presents several less conservative stability criteria, in which the time-scale time derivative of Lyapunov function can be positive or non-negative. To demonstrate the effectiveness of the theoretic results, a numerical example about non-continuous and non-discrete time-delay systems is given.

Stability and steady state analysis of control and safety systems of Nuclear Power Plants

Control Systems are the first layer of safety in Nuclear Power Plants, the failure of which invokes Safety Systems. The failure of safety systems can lead to radiation exposure to the public. Therefore, it is essential to ensure the stability of such systems. This paper proposes an effective methodology for stability and steady state analysis of control and safety systems of Nuclear Power Plants. The methodology includes Petri net modeling and analysis of its dynamic behavior. Despite of its simplicity, it is very accurate. The application of the proposed techniques is shown and validated on a reactor protection system, which is under operation in six Nuclear Power Plants.

Non-Smooth Projected Primal-Dual Dynamical Approach to Solve the Extended Fermat-Torricelli Problem

The problem of finding a point in R <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> , from which the sum-of-distances to a finite number of nonempty, closed and convex sets is minimum is called generalized Fermat-Torricelli Problem (FTP). In applications, along with the point that minimizes sum-of-distances, it is important to know the points in the convex sets at which the minimum sum-of-distances is achieved. Various formulations existing in literature do not involve finding the optimal points in the convex sets. In this letter, we formulate a non-smooth convex optimization problem, with both the point/set of points which yields the minimum sum-of-distances as well as the corresponding points in the convex sets as primal variables. We term this problem as extended FTP (eFTP). We adopt non-smooth projected primal-dual dynamical approach to solve this problem. The proposed dynamical system can exhibit a continuum of equilibria. Hence we show semistability of the set of optimal points, which is the pertinent notion of stability for such systems. A distributed implementation of the primal-dual dynamical system is also presented in this letter. Four illustrative examples are considered for the simulation based validation of the solution proposed for eFTP.

Stabilisation of hybrid stochastic systems with Lévy noise by discrete-time feedback control

This paper is devoted to deal with the stabilisation problems of continuous-time hybrid stochastic systems (often described by stochastic differential equations with Markovian switching) with Lévy noise by feedback controls based on discrete-time state observations. There are so far few results on the stabilisation of continuous-time hybrid stochastic systems with Lévy noise based on discrete-time state observations, despite the stabilisation of stochastic systems by discrete-time feedback controls has been investigated in general. Precisely, it is discussed the stabilisation in the sense of -stability, asymptotic stability, mean-square exponential stability and almost sure exponential stability for such systems. It is also presented an upper bound on the duration τ between two consecutive state observations by means of the Lyapunov function. Two examples are given to illustrate the obtained results.

Analysis of the Task Assignment based on Guessing Size policy

We study the Task Assignment based on Guessing Size (TAGS) policy in a parallel and homogeneous server system. The policy parameters are the number of servers h and a set of cutoffs s1<s2,ldots,sh−1. In this policy, all the incoming jobs are routed to the first server and jobs are run up to s1 time units. If they complete they leave the system, but jobs that do not complete after s1 time units are killed and moved to the end of the queue of the second server, where service starts from scratch. Likewise, jobs that are executed in server i and complete service before si units of time, leave the system, whereas jobs that do not complete are killed and routed to the next server. We first study the stability of such system and provide a precise utilization threshold for the existence of stable parameters for a given job size distribution. We compute the threshold for several families of distributions and provide bounds for others. We show that TAGS is most stable for bounded Pareto distributions with parameter α=1. Besides, we provide tight bounds on the performance of the TAGS policy where the cutoffs are chosen to minimize average waiting time in the asymptotic regime where the largest job size tends to infinity for the Bounded Pareto distribution and the system load smaller than one. In this case, we show that the performance ratio between TAGS and a version called SITA which does require knowledge of job size is at most 2. We then consider more broadly the same asymptotic regime and consider a bound on the average waiting time for any distribution. This is compatible with having a conservative policy which will work well for any job size distribution. We show rather tight upper and lower bounds which again match those of SITA up to a factor of 2. These bounds are considerably lower than the corresponding bounds of competing policies such as Random or Least Work Remaining. We also show that for all these policies the bounded Pareto distribution with α=1 is close to being the worst possible among all distributions with the same job size range. We show using the stability results that in the same regime, if we increase the load the gap between SITA and TAGS grows dramatically and eventually, the TAGS system cannot be stabilized. The conclusion from all our analysis is that TAGS is best used as a conservative policy with minimal requirements on small systems with relatively low utilization and where the range of job sizes is large.

Robust stability of output feedback controlled fractional-order systems with structured uncertainties in all system coefficient matrices

This paper proposes a new necessary and sufficient condition for the robust stability of output feedback controlled fractional-order systems with structured uncertainties in all system coefficient matrices by using μ-analysis and the Kronecker product. The robust stability problems are converted to the judgment of the singularity of the matrices with uncertainties. Furthermore, the explicit robustness bounds of preserving the asymptotical stability of such systems are established based on the above condition. Finally, the proposed results are illustrated by two numerical examples.

Mean Square Stability of Impulsive Stochastic Delayed Reaction-Diffusion Equations via Comparison Principle with Razumikhin Method

This paper investigates the mean square stability problem for impulsive stochastic delayed reaction-diffusion equations. By employing stochastic analysis theory, impulsive differential inequality technique and Razumikhin method, comparison principle for impulsive stochastic delayed reaction-diffusion equations is firstly established. Then, by using the comparison principle, some sufficient conditions are derived to ensure the mean square stability, mean square uniform stability, mean square asymptotic stability and mean square exponential stability of such systems. Finally, an example is provided to show the effectiveness of the proposed results.

Sponge symbiosis is facilitated by adaptive evolution of larval sensory and attachment structures in barnacles.

Symbiotic relations and range of host usage are prominent in coral reefs and crucial to the stability of such systems. In order to explain how symbiotic relations are established and evolve, we used sponge-associated barnacles to ask three questions. (1) Does larval settlement on sponge hosts require novel adaptations facilitating symbiosis? (2) How do larvae settle and start life on their hosts? (3) How has this remarkable symbiotic lifestyle involving many barnacle species evolved? We found that the larvae (cyprids) of sponge-associated barnacles show a remarkably high level of interspecific variation compared with other barnacles. We document that variation in larval attachment devices are specifically related to properties of the surface on which they attach and metamorphose. Mapping of the larval and sponge surface features onto a molecular-based phylogeny showed that sponge symbiosis evolved separately at least three times within barnacles, with the same adaptive features being found in all larvae irrespective of phylogenetic relatedness. Furthermore, the metamorphosis of two species proceeded very differently, with one species remaining superficially on the host and developing a set of white calcareous structures, the other embedding itself into the live host tissue almost immediately after settlement. We argue that such a high degree of evolutionary flexibility of barnacle larvae played an important role in the successful evolution of complex symbiotic relationships in both coral reefs and other marine systems.

Application of frequency stability criterion for analysis of dynamic systems with characteristic polynomials formed in j1/3 basis

This paper considers the stability of dynamical systems described by differential equations with fractional derivatives. In contrast to a number of works, where the differential equation describing the system may have a set of different values ​​of fractional derivatives, and the characteristic polynomial is formed on the basis of the least common multiple for the denominators of these indicators, this article proposes forming such a polynomial in a specific j¹/³ basis and studying the stability of systems with such fractional description based on the resulting rotation angles of Hn(jl/mω) vector at a frequency change from zero to infinity. This technique is similar to the investigation of system stability by frequency criteria used for a similar problem in describing the system by differential equations in integer derivatives. The application of characteristic polynomials formed in the j¹/³ basis for the description of the processes in dynamic systems and the analysis of the stability of such systems on the basis of the frequency criterion are the essence of the scientific novelty of this paper. The article contains the following sections: problem statement, work purpose, presentation of the research material, conclusions, list of references.

On stabilization of an automaton model of migration processes

AbstractA dynamic system of cities with migrants is considered. The wage function is each city depends on the number of migrants in the city. The system is modeled by an automaton whose state is the vector consisting of the numbers of migrants in the cities. The transition function of the automaton reflects the conditions for transfers of migrants between cities. The system stabilizes if the moves are stopped at some point. We find conditions for stabilization of such system depending on the restrictions on the wage function and the automaton transition function. It is shown that if the functions of wages are strictly decreasing, if their ranges are disjoint, and if the transition function is defined so that a migrant moves to another city if and only if its salary increases, then the system necessarily stabilizes and its final state depends only on the total number of migrants and does not depend on their initial distribution over the cities. However, if the transition function is changed so that a migrant moves also if its salary is preserved, but the total wages in all cities are increased, then a monotonous decrease in the wage functions is sufficient for stabilization of the system.

Self-excited vibrations due to viscoelastic interactions

Self-excited vibrations represent a big concern in engineering, particularly in automotive, railway and aeronautic industry. Many lumped models have been proposed over the years to analyze the stability of such systems. Among the instability mechanisms a falling characteristic of the friction law and mode coupling have been shown to give friction-excited oscillations. The mass-on-moving-belt system has been studied extensively in Literature, very often adopting a prescribed form of the friction law and linearizing the contact stiffness. Instead, in this work, the case of a spherical oscillator excited by a moving viscoelastic halfspace is considered. The friction law and the nonlinear normal contact stiffness have been computed via boundary element numerical simulations for varying substrate velocity and indentation depth, then they have been adopted in time-marching dynamical numerical simulations. It is shown that the horizontal and vertical dynamics of the oscillator are tightly connected each other through the viscoelastic substrate. Furthermore, for certain normal forces/substrate velocity, the system has multiple stable solutions, which may include lift-off of the oscillator, which are selected based solely on the system initial conditions.

Practical Stability and Integral Stability for Singular Differential Systems with Maxima

In this paper, we introduce various definitions of practical stability and integral stability for nonlinear singular differential systems with maxima and give criteria of stability for such systems via the Lyapunov method and comparison principle.

A Stabilizing Centralized Controller for On-Chip Power Delivery Networks

A major challenge currently facing integrated systems, such as microprocessors and systems-on-chip is power delivery. With increasing system size and complexity, multiple voltage regulators are often needed for a single power domain. This connection raises non-trivial stability issues that often render the system useless. It is therefore of great practical interest to tackle the stability of such systems. This brief proposes the design of a centralized controller with the aim of rendering such power delivery networks (PDNs) stable without compromising their performance. Theoretical results are confirmed with extensive transistor-level simulations and demonstrate that the controller is capable of stabilizing PDNs with much greater area efficiency than conventional techniques.

Influence of desialylation of caseinomacropeptide on the denaturation and aggregation of whey proteins

The effect of the addition of caseinomacropeptide (CMP) or desialylated CMP on the heat-induced denaturation and aggregation of whey proteins was investigated in the pH range 3 to 7 after heating at 80°C for 30 min. The rate and temperature of denaturation, the extent of aggregation, and the changes in secondary structure of the whey proteins heated in presence of CMP or desialylated CMP were measured. The sialic acid bound to CMP favored the denaturation and aggregation of whey proteins when the whey proteins were oppositely charged to CMP at pH 4. A transition occurred at pH 6, below which the removal of sialic acid enhanced the stabilizing properties of CMP against the denaturation and aggregation of the whey proteins. At pH >6, the interactions between desialylated CMP and the whey proteins led to more extensive denaturation and aggregation. Sialic acid bound to CMP influenced the denaturation and aggregation behavior of whey proteins in a pH-dependent manner, and this should be considered in future studies on the heat stability of such systems containing CMP.

Resilience Analysis for Double Spending via Sequential Decision Optimization

Recently, diverse concepts originating from blockchain ideas have gained increasing popularity. One of the innovations in this technology is the use of the proof-of-work (PoW) concept for reaching a consensus within a distributed network of autonomous computer nodes. This goal has been achieved by design of PoW-based protocols with a built-in equilibrium property: If all participants operate honestly then the best strategy of any agent is also to follow the same protocol. However, there are concerns about the stability of such systems. In this context, the analysis of attack vectors, which represent potentially successful deviations from the honest behavior, turns out to be the most crucial question. Naturally, stability of a blockchain system can be assessed only by determining its most vulnerable components. For this reason, knowing the most successful attacks, regardless of their sophistication level, is inevitable for a reliable stability analysis. In this work, we focus entirely on blockchain systems which are based on the proof-of-work consensus protocols, referred to as PoW-based systems, and consider planning and launching an attack on such system as an optimal sequential decision-making problem under uncertainty. With our results, we suggest a quantitative approach to decide whether a given PoW-based system is vulnerable with respect to this type of attack, which can help assessing and improving its stability.

The stability of differential-difference equations with proportional time delay. I. Linear controlled system

The article considers a controlled system of linear differential-difference equations with a linearly increasing delay. Sufficient conditions for the asymptotic stability of such systems are known; however, general conditions for the stabilizability of controlled systems and constructive algorithms for constructing stabilizing controls have not yet been obtained. For a linear differential-difference equation of delayed type with linearly increasing delay, the canonical Zubov transformation is applied and conditions for the stabilization of such systems by static control are derived. An algorithm for checking the conditions for the existence of a stabilizing control and for its constructing is formulated. New theorems on stability analysis of systems of linear differential-difference equations with linearly increasing delay are proven. The results obtained can be applied to the case of systems with several proportional delays.