General Stability Conditions Research Articles

Two-Higgs-doublet model effective field theory

We construct the general two-Higgs doublet model effective field theory where the effects of additional new physics are parametrized by operators up to mass dimension-six. We further transform this effective theory to the Higgs basis and provide matching of the Wilson coefficients between the two descriptions. We illustrate the advantages of the Higgs basis which include the separation of operators that modify standard model couplings and masses from operators that contribute to scattering processes only, transparent correlations between scattering processes resulting from the same operator, and derivation of correlations between different operators in specific UV completions. For completeness, we also construct specific versions corresponding to four types of two-Higgs-doublet models: type-I, -II, -X, and -Y, distinguished by Z2 symmetries which restrict the couplings of the Higgs doublets to standard model fermions. Furthermore, we derive general vacuum and stability conditions of the scalar potential in the presence of higher-dimensional terms. Published by the American Physical Society 2024

Asynchronous control of networked periodic piecewise linear systems under time-varying transmission delay

This paper studies the stability of networked periodic piecewise linear systems (NPPLSs) of which communication channels are subject to a time-varying transmission delay. Under data-sampling, the NPPLS is modeled as an asynchronous controlled periodic piecewise linear system with time-varying input delay, where the interval of asynchronous control in each subsystem is uncertain but bounded. Aimed at obtaining less conservative stability and synthesis results when tackling the uncertain switching, the dwell time of each subsystem is divided into three subintervals according to the asynchronous control interval and the maximum delay assumption. In this way, it allows the construction of piecewise Lyapunov functionals for one subsystem, the piecewise Lyapunov functionals capture different dynamic characteristics in each subinterval. Using this approach, general stability conditions of NPPLSs are derived. Then, by constructing Lyapunov functionals as a set of delay-dependent time-varying functionals, tractable exponential stability conditions of NPPLSs under transmission delay are developed using a scaling technique. Due to the coupling of the decision variables in the conditions, an iterative algorithm is proposed to solve the periodic controller gains. A numerical example is provided to illustrate the merits of the obtained controllers.

Investigation of electronic, elastic, dynamical, thermodynamic and thermoelectric properties of Cobalt based half-Heusler compounds

Heusler compounds have attracted remarkable attention from scientists over the year by virtue of their peculiarity and suitability in multi-functional applications. In the current study, the structural, elastic, dynamical, thermodynamic and thermoelectric properties of CoMSb (M = V, Nb and Ta) half-Heusler compounds were computed. Projector augmented-wave (PAW) pseudopotentials with PBE exchange correlation functional have been used to obtain the results for the studied compounds. The computed elastic constants satisfy the general stability condition based on the cubic symmetry and endorse the ductile nature of the compounds. The CoVSb compound is predicted to be ferromagnetic half-metallic compound while CoNbSb and CoTaSb are non-magnetic compounds. The dynamical properties revealed the dynamical stability in CoVSb and CoTaSb compounds while the imaginary frequency observed at W⟶L⟶Γ predicts instability in CoNbSb compound. The thermodynamic properties for the compounds were reported. The thermoelectric properties were calculated based on the results obtained from electronic structure using semi-classical Boltzmann theory. The ductile nature and the figure of merit computed predict CoMSb (M = V, Nb and Ta) are relatively good for thermoelectric application.

Interconnected Systems Modelling in Food Industry: General Solution Scheme and Stability Conditions for Linear Time-Invariant Systems

The problem of simulating complex systems, such as production lines, industrial plants, food processing, etc., today represents an opportunity that brings with it the great advantage of limiting design costs. However, nowadays the designer, after defining and implementing the mathematical models of the studied process, may need to rebuild the whole simulation framework because he needs to modify the model of even just one subsystem. It is for this reason that in this paper, a new framework for the use of Individual Subsystem Models (ISM) for the modelling and simulation of interconnected systems has been studied and implemented. Furthermore, the study of the state of the art has revealed the lack of efficient and sufficiently general numerical algorithms, but, at the same time, it is simple to use to solve the algebraic-differential equations deriving from the ISM simulation. The proposed new approach follows the paradigm of co-simulation methods, including graph theory methods, to solve the general ISM simply and efficiently. In this approach, each subsystem is required to have its own representation independently of the other subsystems. In this way, it is always possible to replace any subsystem whenever an updated representation becomes available, making maintenance and evolution of the entire ISM flexible. Our framework calls each subsystem separately in an optimal (suboptimal) order based on the structure of the graph. Each calculated output is transferred to the input of the next subsystem in the chosen. The general procedure has been validated in the context of Linear and Time-Invariant ISMs: in these hypotheses, the stability conditions have been calculated and numerical tests have been performed which show the effectiveness of the proposed approach.

Two-timescale stochastic gradient descent in continuous time with applications to joint online parameter estimation and optimal sensor placement

In this paper, we establish the almost sure convergence of two-timescale stochastic gradient descent algorithms in continuous time under general noise and stability conditions, extending well known results in discrete time. We analyse algorithms with additive noise and those with non-additive noise. In the non-additive case, our analysis is carried out under the assumption that the noise is a continuous-time Markov process, controlled by the algorithm states. The algorithms we consider can be applied to a broad class of bilevel optimisation problems. We study one such problem in detail, namely, the problem of joint online parameter estimation and optimal sensor placement for a partially observed diffusion process. We demonstrate how this can be formulated as a bilevel optimisation problem, and propose a solution in the form of a continuous-time, two-timescale, stochastic gradient descent algorithm. Furthermore, under suitable conditions on the latent signal, the filter, and the filter derivatives, we establish almost sure convergence of the online parameter estimates and optimal sensor placements to the stationary points of the asymptotic log-likelihood and asymptotic filter covariance, respectively. We also provide numerical examples, illustrating the application of the proposed methodology to a partially observed Beneš equation, and a partially observed stochastic advection-diffusion equation.

Stability analysis of delayed neural networks based on improved quadratic function condition

The stability of a class of neural networks (NNs) with time-varying delay is explored in this work. The characteristics of integral inequalities are considered, and the general stability condition (GSC) of delayed NNs avoiding high-order delay is given in the form of quadratic functions. For the GSC of NNs, under the number of decision variables remains unchanged, the information of time-delay and its derivatives are further excavated by delay-partitioning approach. Meanwhile, the free-moving points are established in each subintervals divided, and the traditional static constraints are transformed into dynamic constraints, which relaxes the feasibility space. Based on these methods, the improved stability criteria are given. Finally, two examples are provided to illustrate the meliority of the method under the same number of decision variables.

No general stability conditions for marine ice-sheet grounding lines in the presence of feedbacks

The “marine ice-sheet instability” hypothesis continues to be used to interpret the observed mass loss from the Antarctic and Greenland ice sheets. This hypothesis has been developed for conditions that do not account for feedbacks between ice sheets and environmental conditions. However, snow accumulation and the ice-sheet surface melting depend on the surface temperature, which is a strong function of elevation. Consequently, there is a feedback between precipitation, atmospheric surface temperature and ice-sheet surface elevation. Here, we investigate stability conditions of a marine-based ice sheet in the presence of such a feedback. Our results show that no general stability condition similar to one associated with the “marine ice-sheet instability” hypothesis can be determined. Stability of individual configurations can be established only on a case-by-case basis. These results apply to a wide range of feedbacks between marine ice sheets and atmosphere, ocean and lithosphere.

Stability analysis for nonlinear switched singular systems via T-S fuzzy modeling

The stability for discrete nonlinear switched singular systems with unstable subsystems is investigated. First, by constructing an appropriate multiple discontinuous Lyapunov function, and utilizing the characteristics of mode-dependent average dwell time switching signals, new stability results for nonlinear switched singular system are established. Then, we adopt the T-S fuzzy modeling method to approximate the nonlinear switched singular systems and get general stability conditions in forms of linear matrix inequalities. Compared to the current results, our technique is more flexible and we also get tighter dwell time boundaries. Furthermore, a numerical example demonstrates the effectiveness of the proposed method.

Novel stability results of multivariable fractional-order system with time delay

This paper deduces some novel asymptotic stability criteria for different forms of multivariable fractional-order systems (MFOS) whose fractional-order parameters are between 0 and 1 with time delays based on M-matrix. First, we extend the general asymptotic stability condition of ordinary systems to MFOS. Then, we investigate into the linear and nonlinear MFOS, then the asymptotic stability criterion of which derived based on M-matrix. Then, for the asymptotically stability study of the relatively complex MFOS with time delay, we also present the asymptotic stability criterion via the new method. In addition, we conduct an in-depth discussion on the stability of MFOS and integer order multivariable systems, and intuitively show the advantages of fractional-order systems through time responses. Compared with the fractional-order comparison principle, the new asymptotic stability criteria have the advantages of fewer restrictions, less conservativeness, and a wider applicability. Finally, four examples which contain MFOS covering different categories are shown.

Relativistic star perturbations in Horndeski theories with a gauge-ready formulation

We present a general framework for studying the relativistic star perturbations on a static and spherically symmetric background in full Horndeski theories. We take a perfect fluid into account as a form of the Schutz-Sorkin action. Our formulation is sufficiently versatile in that the second-order actions of perturbations in odd- and even-parity sectors are derived without choosing particular gauge conditions, so they can be used for any convenient gauges at hand. The odd-parity sector contains one dynamical gravitational degree of freedom coupled to a time-independent four velocity of the fluid. In the even-parity sector there are three dynamical perturbations associated with gravity, scalar field, and matter sectors, whose equations of motion are decoupled from other nondynamical perturbations. For high radial and angular momentum modes, we obtain the propagation speeds of all dynamical perturbations and show that the perfect fluid in the even-parity sector has a standard sound speed affected by neither gravity nor the scalar field. Our general stability conditions and perturbation equations of motion can be directly applied to the stabilities of neutron stars and black holes as well as the calculations of their quasinormal frequencies.

Absolute Exponential Stability for Switching Positive Systems With Time-Delay Based on the Φ-Dependent ADT Strategy

The absolute exponential stability problem for the continuous- and discrete-time, respectively, switching positive nonlinear time-delay system is investigated under the nonlinearity of systems satisfying a certain sector condition in this paper. Two multiple co-positive Lyapunov-Krasovskii functionals (MCLKF) of such systems are constructed for the continuous- and discrete-time contexts respectively. By using the MCLKF and the Φ-dependent average dwell time switching strategy, more general stability conditions compatible with some existing works are established. Furthermore, the obtained results are generalized to other types of systems. A numerical example, finally, implies the validity and significance of the results proposed.

On the Backward Path Tracking Control of N-Trailer Systems

This paper considers the lateral control of articulated wheeled vehicles in backward motion. The parameterized articulated vehicle is composed of a car-like truck and N passive trailers, resulting in one single steerable axle. First a nonlinear path tracking control law based on exact linearization of an offset model is reviewed and the general stability conditions of such systems is presented. Second, a stability analysis for some vehicle cases is performed and verified in simulation. The possible application of this path tracking control law in real world articulated vehicles is discussed, and its limitations are shown.

Generalized stability conditions for host–parasitoid population dynamics: Implications for biological control

Discrete-time models are the traditional approach for capturing population dynamics of insects living in the temperate regions of the world. We revisit classical discrete-time models of host–parasitoid population dynamics and provide novel results on the stability of the population dynamics. Discrete-time host–parasitoid models are characterized by update functions that connect the population densities from one year to the next, and a host escape response — the fraction of hosts escaping parasitism each year. For a general class of models we show that the stability can be simply characterized in terms of two quantities: the rate at which the host equilibrium changes with the host’s growth rate, and the sensitivity of the host’s escape response to the host density. Interestingly, stability is more likely to arise when the escape response is a decreasing function of the host density rather than an increasing function. Moreover, if the host’s escape response only depends on the parasitoid population density then the stability condition is further simplified to the host equilibrium density being an increasing function of the host’s reproduction rate. We interpret several mechanisms known for stabilizing host–parasitoid population dynamics in the context of these generalized stability conditions. Next, we introduce a hybrid approach for obtaining the update functions by solving ordinary differential equations that mechanistically capture the ecological interactions between the host and the parasitoid. This hybrid approach is used to study the suppression of host density by a parasitoid. Our analysis shows that when the parasitoid attacks the host at a constant rate, then the host density cannot be suppressed beyond a certain point without making the population dynamics unstable. In contrast, when the parasitoid’s attack rate increases with increasing host density (Type III functional response), then the host population density can be suppressed to arbitrarily low levels while maintaining system stability. These results have important implications for biological control where parasitoids are introduced to eliminate a pest that is the host species for the parasitoid.

Complex dynamical behavior and numerical simulation of a Cournot-Bertrand duopoly game with heterogeneous players

In this paper, we consider the Cournot-Bertrand duopoly mixed competition model, which is characterized by different decision-making variables and different objective functions of the two enterprises. This form of competition is more consistent with the complex actual economic market. The general stability conditions of the four equilibria are given and analyzed with eigenvalues and Jury criterion, so that enterprise decision makers could choose appropriate parameters to determine the development of the enterprise. Under the specific parameter conditions, the stability conditions are analyzed and demonstrated in detail by using two-dimensional bifurcation diagrams, stable region diagrams and bifurcation curves. Many fractal Arnold's tongues are found in two-dimensional bifurcation diagrams. These tongues are associated with the Neimark-Sacker bifurcation of the fixed point and are arranged in accordance with the organization law of the periodic tree of the Stern-Brocot tree, which is helpful for us to analyze the transitions of system between period and chaos. With the help of the basin of attraction, the coexistence of attractors is analyzed, on which the decision maker can choose the initial conditions that are beneficial to the development of the enterprise. We also analyze the topology structure of basin of attraction and the formation mechanism of holes in the basin of attraction by using the theory of critical curve and noninvertible map.

On General Conditions for Uniqueness and Stability of Sparse Tensor Signal Reconstruction

This paper deals with a fundamental aspect of the inverse problem of robustly reconstructing sparse tensor signals via convex optimization. The traditional vector signal model is extended to tensor model and tensor-space based convex optimization methods are applied to establish the critical results. In particular, by means of some innovative sub-differential analysis for tensor norms and convex geometric analysis in normed tensor space, sufficient conditions to guarantee uniqueness and stability of sparse tensor signal reconstruction are established. In comparison with most current works based on vector signal model (1-order tensor), these conditions are more general and more applicable to tensor signals. Also will these conditions be helpful for establishing practical algorithms for reconstructing high-order sparse tensor signals which are emerging in various data-intensive intelligent applications.

Sensitivity Analysis for the Stationary Distribution of Reflected Brownian Motion in a Convex Polyhedral Cone

Reflected Brownian motion (RBM) in a convex polyhedral cone arises in a variety of applications ranging from the theory of stochastic networks to mathematical finance, and under general stability conditions, it has a unique stationary distribution. In such applications, to implement a stochastic optimization algorithm or quantify robustness of a model, it is useful to characterize the dependence of stationary performance measures on model parameters. In this paper, we characterize parametric sensitivities of the stationary distribution of an RBM in a simple convex polyhedral cone, that is, sensitivities to perturbations of the parameters that define the RBM—namely the covariance matrix, drift vector, and directions of reflection along the boundary of the polyhedral cone. In order to characterize these sensitivities, we study the long-time behavior of the joint process consisting of an RBM along with its so-called derivative process, which characterizes pathwise derivatives of RBMs on finite time intervals. We show that the joint process is positive recurrent and has a unique stationary distribution and that parametric sensitivities of the stationary distribution of an RBM can be expressed in terms of the stationary distribution of the joint process. This can be thought of as establishing an interchange of the differential operator and the limit in time. The analysis of ergodicity of the joint process is significantly more complicated than that of the RBM because of its degeneracy and the fact that the derivative process exhibits jumps that are modulated by the RBM. The proofs of our results rely on path properties of coupled RBMs and contraction properties related to the geometry of the polyhedral cone and directions of reflection along the boundary. Our results are potentially useful for developing efficient numerical algorithms for computing sensitivities of functionals of stationary RBMs.

A Generalized Thermodynamic Criterion of Equilibrium

Thermodynamic functions, such as entropy, underlie macroscopic and microscopic thermodynamics, and supply essential tools to many related disciplines. Determining a steady-state process is one of the basic roles of the thermodynamic criterion of equilibrium. However, the classical thermodynamic criterion of equilibrium requires second-order differentiable functions, that is, a strong constraint in mathematics. To relax this constraint, convex analysis is applied to reformulate a generalized thermodynamic criterion of equilibrium only with first-order differentiable requirement. Then, it is proved that this generalized stability condition is a necessary but insufficient condition for the classical one. In addition to isolated systems, the corresponding criteria under various constraints are given. This theorem works in some thermodynamic systems which are only first-order differentiable, such as second-order phase-transitions. To indicate that this theorem determines the direction of spontaneous change and the stability of equilibrium, different thermodynamic problems are demonstrated with the generalized criterion, thereby revealing the usefulness of this theorem.

Charged scalar quasi-normal modes for higher-dimensional Born\u2013Infeld dilatonic black holes with Lifshitz scaling

We study quasi-normal modes for a higher dimensional black hole with Lifshitz scaling, as these quasi-normal modes can be used to test Lifshitz models with large extra dimensions. We analyze quasi-normal modes for higher dimensional dilaton-Lifshitz black hole solutions coupled to a non-linear Born–Infeld action. We will analyze the charged perturbations for such a black hole solution. We will first analyze the general conditions for stability analytically, for a positive potential. Then, we analyze this system for a charged perturbation as well as negative potential, using the asymptotic iteration method for quasi-normal modes.

General condition for exponential stability of thermoelastic Bresse systems with Cattaneo's law

In this paper, we give a new and more general sufficient condition for exponential stability of thermoelastic Bresse systems with heat flux given by Cattaneo's law acting in shear and longitudinal motion equations. This condition, which we also prove to be necessary in some special cases, is given by a relation between the constants of the system and generalizes the well-known equal wave speed condition.

Stability of Switched Differential Repetitive Processes and Iterative Learning Control Design

In this paper general stability conditions of differential nonlinear repetitive processes with switching are obtained. The approach is based on the development of a method that uses vector Lyapunov functions and the properties of the counterpart of its divergence. The obtained results are applied to iterative learning control design for switched linear system. An example that demonstrate effectiveness of the new design is given.