L. Berezansky, L. Idels
We introduce a delay nonlinear differential equation model which describes how fish are harvested. In our previous studies we investigated the persistence of that equation and existence of a periodic solution for this equation. Here we study the stability (local and global) of the periodic solutions of that equation.
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In this paper, the stability analysis of quaternion-valued neural networks (QVNNs) with both leakage delay and additive time-varying delays is proposed. By employing the Lyapunov-Krasovskii functional method and fully considering the relationship between time-varying delays and upper bounds of delays, some sufficient criteria are derived based on reciprocally convex method and several inequality techniques. The stability criteria are established in two forms: quaternion-valued linear matrix inequalities (QVLMIs) and complex-valued linear matrix inequalities (CVLMIs), in which CVLMIs can be dir…
Stabilization of linear systems with multiple unknown time-varying input delays by linear time-varying feedback
针对时滞信息未知的线性多重时变输入时滞系统，本文提出基于参数 Lyapunov 方程解的线性时变状态反馈控制器及输出反馈扩展，证明了闭环系统渐近稳定，且控制器设计完全独立于时滞知识，易于实现。
Understanding how delayed information impacts queueing systems is an important area of research. However, much of the current literature neglects one important feature of many queueing systems, namely non-stationary arrivals. Non-stationary arrivals model the fact that customers tend to access services during certain times of the day and not at a constant rate. In this paper, we analyze two two-dimensional deterministic fluid models that incorporate customer choice behavior based on delayed queue length information with time varying arrivals. In the first model, customers receive queue length …
On Time-Varying Delayed Stochastic Differential Systems with Non-Markovian Switching Parameters
针对以往研究局限于平稳遍历切换的不足，本文用离散适应过程与 Cox 过程统一建模非马尔可夫、非平稳、非遍历的时变延迟随机微分系统，并给出更严谨、更一般的稳定性分析结果。
The problem of p-th moment stability for time-varying stochastic time-delay systems with Markovian switching is investigated in this paper. Some novel stability criteria are obtained by applying the generalized Razumikhin and Krasovskii stability theorems. Both p-th moment asymptotic stability and (integral) input-to-state stability are considered based on the notion and properties of uniformly stable functions and the improved comparison principles. The established results show that time-derivatives of the constructed Razumikhin functions and Krasovskii functionals are allowed to be indefinit…
Absolute exponential stability problem of delay time-varying systems (DTVS) with sector-bounded nonlinearity is presented in this paper. By using the comparison principle and properties of positive systems we derive several novel criteria of absolute exponential stability, for both continuous-time and discrete-time nonlinear DTVS. When applied to the time-invariant case, the obtained stability criteria are shown to cover and extend some previously known results, including, in particular, the result due to S.K. Persidskii in Ukrainian Mathematical Journal, vol. 57(2005). The theoretical results…
Stability of the zero solution plays an important role in the investigation of positive systems. In this note, we revisit the $μ$-stability of positive nonlinear systems with unbounded time-varying delays. The system is modelled by continuous-time differential equations. Under some assumptions on the nonlinear functions like homogeneous, cooperative, nondecreasing, we propose a novel transform, by which the nonlinear system reduces to a new system. Thus, we analyze its dynamics, which can simplify the nonlinear homogenous functions with respect to (w.r.t.) arbitrary dilation map to those w.r.t…
In this report, we develop a semistability analysis framework for nonlinear systems with bounded time-varying delays with applications to stability analysis of multiagent dynamic networks with consensus protocols in the presence of unknown heterogeneous time-varying delays along the communication links. We show that for such a nonlinear system having nonisolated equilibria, if the system asymptotically converges to a constant time-delay system and this new system is semistable, then the original time-varying delay system is semistable. In proving our results, we extend the limiting differentia…
Problem of adaptive state observer synthesis for linear time-varying (LTV) system with unknown time-varying parameter and delayed output measurements is considered. State observation problem has attracted the attention of many researchers $[4]$. In this paper the results proposed in the $[2]$, $[9]$, $[10]$ are developed. It is supposed that the state matrix can be represented as sum of known and unknown parts. Output vector is measured with known constant delay. An adaptive identification algorithm which reconstructs unknown state and unknown time varying parameter is proposed.
We first propose the concept of Stepanov-like weighted pseudo-almost automorphic on time-space scales and we apply this type of oscillation to high-order BAM neural networks with mixed delays. Then, we study the existence and exponential stability of Sp-weighted pseudo almost automorphic on time-space scales solutions for the suggested system. Some criteria assuring the convergence are proposed. Our method is mainly based on the Banachs fixed point theorem, the theory of calculus on time scales and the Lyapunov-Krasovskii functional method. Moreover, a numerical example is given to show the ef…
In this paper, we study asynchronous consensus problems of continuous-time multi-agent systems with discontinuous information transmission. The proposed consensus control strategy is implemented only based on the state information at some discrete times of each agent's neighbors. The asynchronization means that each agent's update times, at which the agent adjusts its dynamics, are independent of others'. Furthermore, it is assumed that the communication topology among agents is time-dependent and the information transmission is with bounded time-varying delays. If the union of the communicati…
Bilateral Solution Bounds and Successive Estimation of Boundedness and Stability Regions for Vector Delay Nonlinear Time-Varying Systems
本文提出了一种基于连续逼近和残差范数估计的方法，用于估计向量时变延迟非线性系统的解范数演变，从而获得双侧界并实现有效的稳定性与有界性分析。
This paper considers $L_2$ and BIBO stability and stabilization issues for systems with time-varying delays which can be of retarded or neutral type. An important role is played by a nominal system with fixed delays which are close to the time-varying ones. Under stability or stabilizability conditions of this nominal system, sufficient conditions are given in order to ensure similar properties for the system with time-varying delays.
In this paper, we consider the almost periodic dynamics of a multispecies Lotka-Volterra mutualism system with time varying delays on time scales. By establishing some dynamic inequalities on time scales, a permanence result for the model is obtained. Furthermore, by means of the almost periodic functional hull theory on time scales and Lyapunov functional, some criteria are obtained for the existence, uniqueness and global attractivity of almost periodic solutions of the model. Our results complement and extend some scientific work in recent years. Finally, an example is given to illustrate t…
In the present paper we investigate the influence of the retarded access by a time-varying delay on the dynamics of delay systems. We show that there are two universality classes of delays, which lead to fundamental differences in dynamical quantities such as the Lyapunov spectrum. Therefore we introduce an operator theoretic framework, where the solution operator of the delay system is decomposed into the Koopman operator describing the delay access and an operator similar to the solution operator known from systems with constant delay. The Koopman operator corresponds to an iterated map, cal…
This paper presents a distributed position synchronization strategy that also preserves the initial communication links for single-integrator multi-agent systems with time-varying delays. The strategy employs a coordinating proportional control derived from a specific type of potential energy, augmented with damping injected through a dynamic filter. The injected damping maintains all agents within the communication distances of their neighbours, and asymptotically stabilizes the multi-agent system, in the presence of time delays. Regarding the closed-loop single-integrator multi-agent system …
In this paper, a kind of neural network with time-varying delays is proposed to solve the problems of quadratic programming. The delay term of the neural network changes with time t. The number of neurons in the neural network is n + h, so the structure is more concise. The equilibrium point of the neural network is consistent with the optimal solution of the original optimization problem. The existence and uniqueness of the equilibrium point of the neural network are proved. Application inequality technique proved global exponential stability of the network. Some numerical examples are given …
Globally Stable Output Feedback Synchronization of Teleoperation with Time-Varying Delays
本文提出了一种全局稳定的远程操作控制策略，通过新颖的增强浸入不变速度观测器消除速度测量需求，实现具有时间变化延迟系统的同步。
In this paper we address the problem of adaptive state observation of affine-inthe-states time-varying systems with delayed measurements and unknown parameters. The development of the results proposed in the [Bobtsov et al. 2021a] and in the [Bobtsov et al. 2021c] is considered. The case with known parameters has been studied by many researchers (see [Sanz et al. 2019, Bobtsov et al. 2021b] and references therein) where, similarly to the approach adopted here, the system is treated as a linear time-varying system. We show that the parameter estimation-based observer (PEBO) design proposed in […
In this paper, we studied the finite time anti-synchronization of master-slave coupled complex-valued neural networks (CVNNs) with bounded asynchronous time-varying delays. With the decomposing technique and the generalized $\{ξ,\infty\}$-norm, several criteria for ensuring the finite-time anti-synchronization are obtained. The whole anti-synchronization process can be divided into two parts: first, the norm of each error state component will change from initial values to $1$ in finite time, then from $1$ to $0$ in fixed time. Therefore, the whole time is finite. Finally, one typical numerical…
In this paper, we study the simultaneous stability problem of a finite number of locally inter-connected linear subsystems under practical constraints, including asynchronous and aperiodic sampling, time-varying delays, and measurement errors. We establish a new Lyapunov-based stability result for such a decentralized system. This system has a particular simple structure of interconnections, but it captures some key characteristics of a large class of intermediate models derived from the consensus analysis of multi-agent systems. The stability result is applicable to the estimation of the maxi…
Sufficient Stability Conditions for Time-varying Networks of Telegrapher's Equations or Difference Delay Equations
本文针对由线性时变边界条件耦合的无损电报方程网络，基于耦合耗散性给出适用于任意 $L^p$-范数的指数稳定性充分条件，并将其推广到一类线性时变差分时滞系统，简化了已有证明。
This paper investigates the robust stability and stabilization analysis of interval fractional-order systems with time-varying delay. The stability problem of such systems is solved first, and then using the proposed results a stabilization theorem is also included, where sufficient conditions are obtained for designing a stabilizing controller with a predetermined order, which can be chosen to be as low as possible. Utilizing efficient lemmas, the stability and stabilization theorems are proposed in the form of LMIs, which is more suitable to check due to various existing efficient convex opt…
Solving optimization problems in multi-agent systems (MAS) involves information exchange between agents. These solutions must be robust to delays and errors that arise from an unreliable wireless network which typically connects the MAS. In today's large-scale dynamic Internet Of Things style multi-agent scenarios, the network topology changes and evolves over time. In this paper, we present a simple distributed gradient based optimization framework and an associated algorithm. Convergence to a minimum of a given objective is shown under mild conditions on the network topology and objective. S…
We study the combined effects of periodically varying carrying capacity and survival rates on the fish population in the ocean (sea). We introduce the Getz type delay differential equation model with a control parameter which describes how fish are harvested. We will modify and extend harvesting model of an exploited fish population to include periodic and rotational harvesting rates. We study the existence of global solutions for the initial value problem, extinction and persistence conditions, and the existence of periodic solutions.
Event-Triggered Stabilization of Nonlinear Systems with Time-Varying Sensing and Actuation Delay
本文研究了使用事件触发控制对具有时间变化延迟的非线性系统进行稳定化的问题。所提出的方法旨在机会性地减少控制更新次数，同时保证稳定化，并基于预测反馈来补偿任意大的已知时间变化延迟。通过Lyapunov方法，我们证明只要在没有时间延迟和采样的情况下，开环系统是全局输入到状态可稳定化的，则闭环系统具有全局渐近稳定性。我们进一步证明所提出的事件触发法则具有均匀下界的事件间隔，因此不会出现Zeno行为。对于可稳定化的线性系统，我们展示了闭环系统的全局指数稳定性，并分析了指数收敛速率与采样频率上界之间的权衡。我们通过仿真展示了这些结果，并检查了所提出的事件触发策略在保证稳定化的系统类别之外的性质。
Memory Resilient Gain-scheduled State-Feedback Control of Uncertain LTI/LPV Systems with Time-Varying Delays
针对具有时变时滞的不确定LTI/LPV系统，提出一种通过状态反馈控制器实现鲁棒镇定且对时滞不确定性具有弹性的方法，并统一了无记忆和精确记忆控制器。
This paper proposes a unified approach for studying global exponential stability of a general class of switched systems described by time-varying nonlinear functional differential equations. Some new delay-independent criteria of global exponential stability are established for this class of systems under arbitrary switching which satisfies some assumptions on the average dwell time. The obtained criteria are shown to cover and improve many previously known results, including, in particular, sufficient conditions for absolute exponential stability of switched time-delay systems with sector non…
An equilibrium of a delay differential equation (DDE) is absolutely stable, if it is locally asymptotically stable for all delays. We present criteria for absolute stability of DDEs with discrete time-delays. In the case of a single delay, the absolute stability is shown to be equivalent to asymptotic stability for sufficiently large delays. Similarly, for multiple delays, the absolute stability is equivalent to asymptotic stability for hierarchically large delays. Additionally, we give necessary and sufficient conditions for a linear DDE to be hyperbolic for all delays. The latter conditions …
In this paper we address the problem of state observation of linear time-varying systems with delayed measurements, which has attracted the attention of many researchers|see [7] and references therein. We show that, adopting the parameter estimationbased approach proposed in [3,4], we can provide a very simple solution to the problem with reduced prior knowledge.
In this contribution, we study an homogeneous class of nonlinear time delay systems with time-varying perturbations. Using the Lyapunov-Krasovskii approach, we introduce a functional that leads to perturbation conditions matching those obtained previously in the Razumikhin framework. The functionals are applied to the estimation of the domain of attraction and of the system solutions. An illustrative example is given.
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