Sufficient Conditions For Stability Research Articles

Practical robust fixed-time containment control for multi-agent systems under actuator faults

This article considers a containment control problem for nonlinear multi-agent systems with nonautonomous leaders under directed topology, where each follower may experience various actuator faults and unknown external disturbances. A practical robust fixed-time fault-tolerant controller is proposed that eliminates the adverse effects of disturbances and actuator faults while achieving the containment control objective within a fixed-time. Independent of initial states, a sufficient condition of practical robust fixed-time stabilization is derived, further relaxing the constraint of robust fixed-time stabilization. The combination of sliding-mode control and event-triggered mechanism in this approach provides better control performance. One advantage of this method is that the sliding-mode band size is no longer dependent on the sampling interval but rather on the triggering function. Another advantage is that the resource costs for handling faults are effectively reduced. Additionally, an adaptive boundary layer technique is designed to avoid chattering phenomenon of the discontinuous controller, which utilizes adaptive parameters to autonomously adjust the width of boundary layer. Zeno behavior analysis and a simulated example are also presented.

Finite-time stabilization of nonlinear time-varying systems involving impulsive action

This article investigates the finite-time stabilization of time-varying impulsive systems by time-varying feedback control. Moreover, the stabilizing and destabilizing effects of impulses on the stability of the system are considered, where the stabilizing impulses are used to regulate the unstable continuous dynamics. In addition, it can be found that the local and global characteristics of the finite-time stability may be affected by the stabilizing impulses. By establishing the relationship among the time-varying gain functions, the system structure and impulsive time sequences, some sufficient conditions for finite-time stability of time-varying systems involving impulsive action are proposed. Furthermore, based on the results mentioned above, a new class of finite-time controllers is designed for time-varying affine systems with external noises. The effectiveness of the proposed results is illustrated by three examples.

Stability and rate of decay for solutions to stochastic differential equations with Markov switching

In this article, we present the almost sure asymptotic stability and a general rate of decay for solutions to stochastic differential equations (SDEs) with Markov switching. By establishing a suitable Lyapunov function and using an exponential Martingale inequality and the Borel-Cantelli theorem, we give sufficient conditions for the asymptotic stability. Also, we obtain sufficient conditions for the construction of two kinds of Lyapunov functions. Finally give two examples to illustrate the validity of our results. For more information see https://ejde.math.txstate.edu/Volumes/2024/01/abstr.html

Bifurcation structure of interval maps with orbits homoclinic to a saddle-focus

UDC 517.9 We study homoclinic bifurcations in an interval map associated with a saddle-focus of (2, 1)-type in Z 2 -symmetric systems. Our study of this map reveals a homoclinic structure of the saddle-focus, with bifurcation unfolding guided by the codimension-two Belyakov bifurcation. We consider three parameters of the map corresponding to the saddle quantity, splitting parameter, and the focal frequency of the smooth saddle-focus in a neighborhood of homoclinic bifurcations. We symbolically encode the dynamics of the map in order to find stability windows and locate homoclinic bifurcation sets in a computationally efficient manner. The organization and possible shapes of homoclinic bifurcation curves in the parameter space are examined, taking into account the symmetry and discontinuity of the map. Sufficient conditions for stability and local symbolic constancy of the map are presented. This study provides insights into the structure of homoclinic bifurcations of the saddle-focus map, furthering comprehension of low-dimensional chaotic systems.

Formula omitted]th moment stability of discrete-time Markov jump systems by extended system method

This paper studies the pth moment stability of discrete-time Markov jump systems by utilizing the extended system method, which is composed of the operator spectrum technique and the ℋ-representation technique. Firstly, some extended systems are constructed by the operator spectrum technique and the ℋ-representation technique to transform the discrete-time Markov jump systems into the extended systems. Furthermore, the relationship in pth moment stability between the extended systems and the stochastic systems is discussed. Next, with the help of the extended systems, the necessary and sufficient conditions for the even-order moment stability, and several sufficient conditions/necessary conditions for the odd-order moment stability are obtained, respectively. Additionally, as applications of the extended system method, observability and detectability in pth moment sense are discussed, and the necessary and sufficient conditions for observability and detectability in even-order moment are obtained, respectively. Finally, several examples are given to illustrate the validity of the results.

Analysis of a free boundary problem for vascularized tumor growth with time delays and almost periodic nutrient supply

<abstract><p>In this research, we have proposed and investigated a time-delayed free boundary problem concerning tumor growth in the presence of almost periodic nutrient supply with angiogenesis. This study primarily focused on examining the impact of almost periodic nutrient supply, angiogenesis, and time delay on tumor growth dynamics. We analyzed the existence, uniqueness, and exponential stability of almost periodic solutions. Furthermore, we established conditions for the disappearance of almost periodic oscillations in tumors. The existence and uniqueness of almost periodic solutions were proven, while sufficient conditions for the exponential stability of the unique solution were established. Finally, computer simulations were employed to illustrate our results.</p></abstract>

Fixed-Time Composite Neural Learning Control of Flexible Telerobotic Systems.

This article is devoted to the fixed-time synchronous control for a class of uncertain flexible telerobotic systems. The presence of unknown joint flexible coupling, time-varying system uncertainties, and external disturbances makes the system different from those in the related works. First, the lumped system dynamics uncertainties and external disturbances are estimated successfully by designing a new composite adaptive neural networks (CANNs) learning law skillfully. Moreover, the fast-transient, satisfactory robustness, and high-precision position/force synchronization are also realized by design of fixed-time impedance control strategies. Furthermore, the "complexity explosion" issue triggered by traditional backstepping technology is averted efficiently via a novel fixed-time command filter and filter compensation signals. And then, sufficient conditions of system controller parameters and fixed-time stability are theoretically given by establishing the Lyapunov stability theorem. Besides, the absolute stability of the two-port networked system under complex transmission time delays is rigorously proved. Finally, simulations are performed with 2-link flexible telerobotic systems under two cases, results are presented to realistically verify the proposed control algorithm available.

Data-driven optimal controller design for sub-satellite deployment of tethered satellite system

<abstract><p>In the paper, we presented a data-driven optimal control method for the sub-satellite deployment of tethered satellite systems during the release phase, with the objective of reducing the libration angle fluctuation during system work. First, the dynamic equation of the tethered satellite system was established and processed dimensionless. Considering the presence of noise when sensors were put on the satellite to measure the libration angle, the corresponding state equation was derived. Next, we estimated the system state using an unscented Kalman filter and established a performance index and the Hamilton function. Based on the index, we designed an optimal control strategy and provided sufficient conditions for the asymptotic stability of the closed-loop system. We used critic-actor neural networks based on measurement data to implement the data-driven control algorithm to approximate the performance index function and the control policy, respectively. Finally, taking a tethered satellite system as an example, a simulation showed that the unscented Kalman filter can effectively estimate the system state and improve the impact of noise on the system, and the proposed optimal control strategy ensured that the tethered satellite system is stable, which shows the applicability and effectiveness of the control strategy in reducing the tether vibration of the disturbed system.</p></abstract>

Competitive Equilibrium Analysis for Renewables Integration in Dynamic Combined Heat and Power Trading Market

With the increasing interdependence among the electricity and district heating systems in economy and physics, this study focuses on the equilibrium analysis of the combined heat and power market (CHPM). Based on the gradient method in game theory, a dynamic model characterizing renewables uncertainty and negotiation process among dominant participants is established. Inspired by modern control theory, the dynamic model can be viewed as state equations in which the actions of participants are control signals, and the system states, such as nodal price and bus voltages, are treated as system state variables. A detailed proof for asymptotic stability around the market equilibrium is derived, and its region of attraction is quantified. The resulting sufficient conditions can also be used to quantify the impact of renewable energy uncertainty and congestion constraints on market stability. The whole trading process is designed to be implemented by distributed algorithms to reduce the computation burden of central authority. Numerical tests on two cases with different scales are conducted to demonstrate the theoretical analysis and the application of the proposed sufficient conditions for market stability.

A Levy process approach coupled to the stochastic Leslie–Gower model

This paper focuses on a two-dimensional Leslie–Grower continuous-time stochastic predator–prey system with Lévy jumps. Firstly, we prove that there exists a unique positive solution of the system with a positive initial value. Then, we establish sufficient conditions for the mean stability and extinction of the considered system. Numerical algorithms of higher order are elaborated. The obtained results show that Lévy jumps significantly change the properties of population systems.

Graph-Based Restricted and Arbitrary Switching for Switched Positive Systems via a Weak CLCLF.

This article studies the stability problem of discrete-time switched positive linear systems (SPLSs) with marginally stable subsystems. Based on the weak common linear copositive Lyapunov function (weak CLCLF) approach, the switching property and the state component property are combined to ensure the asymptotic stability of SPLSs under three types of switching signals. First, considering the transfer-restricted switching signal described by the switching digraph, novel cycle-dependent joint path conditions are proposed in combination with state component digraphs. Second, under the time interval sequence, two types of path conditions are constructed for designing switching schemes. Third, necessary and sufficient conditions for the asymptotic stability of SPLSs under arbitrary switching are established. Finally, three examples are provided to illustrate the effectiveness of the proposed method.

Partial-Information-Based Non-Fragile Intermittent Estimator for Microgrids With Semi-Aperiodic DoS Attacks: Gain Stochastic Float

This paper mainly focuses on the problem of nonfragile intermittent estimate tracking in microgrid systems with denial of service (DoS) attacks and gain fluctuation. Different from the common DC/AC microgrid system, the microgrid system studied in this paper involves large grid control and power line communication technology, which is more in line with the actual operating environment. Simultaneously, aiming at the occurrence of network-induced DoS attacks, an intermittent estimator based on partial measure information under cyber-attacks is designed. More importantly, instead of the existing single aperiodic or periodic DoS attacks, the DoS attacks scheme presented in this paper is semi-periodic DoS attacks whose the attack range is aperiodic and the attack width is certain. Furthermore, a variable obeying the Bernoulli distribution is proposed to characterize the randomly occurring gain fluctuation, in which the no-fragile observation is stochastic uncertain. Then, two sufficient conditions of stochastic stability of observation error system of microgrid are devised with the assistance of two different Lyapunov theories. Finally, the rationality of the developed theoretical method is verified by a numerical example.

Asymptotic Stability of Delayed Boolean Networks With Random Data Dropouts.

In real networks, communication constraints often prevent the full exchange of information between nodes, which is inevitable. This brief investigates the problem of time delay and randomly missing data in Boolean networks (BNs). A Bernoulli random variable is assigned to each node to characterize the probability of data packet dropout. Time delay and missing data are modeled by independent random variables. A novel data-sending rule that incorporates both communication constraints is proposed. An augmented system, comprising current states, delayed information, and successfully transmitted data, is established for theoretical analysis. Using the semitensor product (STP), the necessary and sufficient condition for asymptotic stability of delayed BNs with random data dropouts is derived. The convergence rate is also obtained.

Stability and Hopf bifurcation of an intraguild prey-predator fishery model with two delays and Michaelis-Menten type predator harvest.

In this paper, we have proposed and investigated an intraguild predator-prey system incorporating two delays and a harvesting mechanism based on the Michaelis-Menten principle, and it was assumed that the two species compete for a shared resource. Firstly, we examined the properties of the relevant characteristic equations to derive sufficient conditions for the asymptotical stability of equilibria in the delayed model and the existence of Hopf bifurcation. Using the normal form method and the central manifold theorem, we analyzed the stability and direction of periodic solutions arising from Hopf bifurcations. Our theoretical findings were subsequently validated through numerical simulations. Furthermore, we explored the impact of harvesting on the quantity of biological resources and examined the critical values associated with the two delays.

Deficit financing and Macroeconomic Performance: the Nigeria experience

Due to the mixed order of integration, the study uses the ARDL model to examine the relationship between deficit financing and the performance of the macroeconomy proxy by GDP in Nigeria over a thirty-year period, from 1990 to 2019. In the model, the inflation rate, the government's fiscal deficit, and the domestic money supply served as stand-ins for deficit financing. And the outcome demonstrates that while the model satisfied the sufficient condition of stability, it failed the necessary condition due to an explosive divergence indicator. Additionally, the variables have a long-term relationship, and based on estimates from the long-run equation, all of the variables have a significant impact on the economy, with the domestic money supply having a positive effect and inflation and the government fiscal deficit having a negative impact.

Об устойчивости и точности конечно-объёмных схем на неравномерных сетках

The paper studies the behavior of high-order finite-volume schemes for the 1D transport equation on non-uniform meshes. We consider finite-volume schemes with a polynomial reconstruction and schemes based on divided differences. We prove a sufficient stability condition on mildly deformed meshes and establish estimates for the solution error.

Quadratic stability of uncertain large-scale networked systems

In this paper, the quadratic stability of continuous-time uncertain large-scale networked systems is considered. The systems are composed of many subsystems distributed in different locations in space and interconnected according to a certain network topology. A computationally efficient sufficient condition for the quadratic stability of large-scale networked systems is established, utilising effectively the block diagonal structure of the system parameter matrix and the sparseness of the subsystem connection matrix (SCM). Furthermore, a stability condition is presented, which is entirely contingent on the parameters of each subsystem. The simulation results show that the obtained conditions have obvious advantages in analysing the quadratic stability of large-scale networked systems.

The Necessary and Sufficient Conditions of Exponential Stability for Heat and Wave Equations with Memory

The Necessary and Sufficient Conditions of Exponential Stability for Heat and Wave Equations with Memory

Synchronization for fractional-order neural networks with unbounded delays

This paper deals with synchronization analysis problem for a class of fractional-order neural networks with unbounded delays. Using the Lyapunov function method combined with fractional Halanay inequality, we derive a novel sufficient condition for asymptotic stability of the error system resulting in two neural networks are synchronized. The obtained conditions are given in terms of linear matrix inequalities, which therefore can be efficiently checked. A numerical example is proposed to illustrate the effectiveness of the obtained results.

Partial stability analysis of linear time-varying perturbed stochastic systems via a refined integral inequality

The Lyapunov approach is one of the most effective and efficient means of studying the partial stability of stochastic systems. A number of authors have analysed the partial practical stability of stochastic differential equations using Lyapunov techniques. Nevertheless, no results are concerned with the partial stability of stochastic systems based on the knowledge of the solution of the system explicitly. This paper has been concerned with the problem of partial practical stability for linear time-varying stochastic perturbed systems. Necessary and sufficient conditions for partial practical uniform exponential stability are given based on generalised Gronwall inequalities, in particular of Gamidov's type. An example is developed to illustrate the obtained results.