Delay-independent Stability Conditions Research Articles

Delay-independent stability of a tri-stable energy harvesting system with time-delayed feedback control

This paper analyzes the delay-independent stability and harvesting performance of a tri-stable vibrational energy harvester (TVEH) with time-delayed feedback control. The dynamical model of the controlled electromechanical TVEH is established, and the method of multiple scales is employed to derive the steady-state response near the primary resonance. The delay-independent stability conditions of the TVEH are obtained using Routh Hurwitz criterion and classical Sturm criterion. The influences of time-delayed feedback control on the TVEH's output and jump phenomena are discussed through the steady-state response. Furthermore, appropriate choices of feedback gains and time delays can ensure the system stability and enhance the output power. The theoretical results are validated through numerical simulations, demonstrating the effectiveness of the proposed control strategy.

Novel Hopf Bifurcation Exploration and Control Strategies in the Fractional-Order FitzHugh–Nagumo Neural Model Incorporating Delay

In this article, we propose a new fractional-order delay-coupled FitzHugh–Nagumo neural model. Taking advantage of delay as a bifurcation parameter, we explore the stability and bifurcation of the formulated fractional-order delay-coupled FitzHugh–Nagumo neural model. A delay-independent stability and bifurcation conditions for the fractional-order delay-coupled FitzHugh–Nagumo neural model is acquired. By designing a proper PDp controller, we can efficaciously control the stability domain and the time of emergence of the bifurcation phenomenon of the considered fractional delay-coupled FitzHugh–Nagumo neural model. By exploiting a reasonable hybrid controller, we can successfully adjust the stability domain and the bifurcation onset time of the involved fractional delay-coupled FitzHugh–Nagumo neural model. This study shows that when the delay crosses a critical value, a Hopf bifurcation will arise. When we adjust the control parameter, we can find other critical values to enlarge or narrow the stability domain of the fractional-order delay-coupled FitzHugh–Nagumo neural model. In order to check the correctness of the acquired outcomes of this article, we present some simulation outcomes via Matlab 7.0 software. The obtained theoretical fruits in this article have momentous theoretical significance in running and constructing networks.

Integrated fault estimation and control for multi-agent systems with external disturbance using delayed relative information

This paper is dedicated to the problem of actuator fault estimation and fault-tolerant control for general linear leader–follower multi-agent systems subject to external disturbance and communication delay. First, the intermediate variable observer is constructed to estimate faults using relative information with symmetric time delays. A contradiction between the convergence speed of estimation error and the time-delay margin is revealed, where quick convergence implies small time-delay margin. As such, the augmented system observer is employed to improve the convergence speed. In the next, integrated scheme is adopted to handle the bi-directional interaction between fault estimation and fault-tolerant control arising from external disturbance and time-varying faults. In addition, we also consider the asymmetric delay case with only transmission delay. The delay-independent stability condition is derived with the use of augmented system observer by virtue of Lyapunov–Krasovskii function and [Formula: see text] robust theories. Finally, the simulation results are presented to verify the effectiveness of proposed method.

Bifurcation Behavior and Hybrid Controller Design of a 2D Lotka–Volterra Commensal Symbiosis System Accompanying Delay

All the time, differential dynamical models with delay has witness a tremendous application value in characterizing the internal law among diverse biological populations in biology. In the current article, on the basis of the previous publications, we formulate a new Lotka–Volterra commensal symbiosis system accompanying delay. Utilizing fixed point theorem, inequality tactics and an appropriate function, we gain the sufficient criteria on existence and uniqueness, non-negativeness and boundedness of the solution to the formulated delayed Lotka–Volterra commensal symbiosis system. Making use of stability and bifurcation theory of delayed differential equation, we focus on the emergence of bifurcation behavior and stability nature of the formulated delayed Lotka–Volterra commensal symbiosis system. A new delay-independent stability and bifurcation conditions on the model are presented. By constructing a positive definite function, we explore the global stability. By constructing two diverse hybrid delayed feedback controllers, we can adjusted the domain of stability and time of appearance of Hopf bifurcation of the delayed Lotka–Volterra commensal symbiosis system. The effect of time delay on the domain of stability and time of appearance of Hopf bifurcation of the model is given. Matlab experiment diagrams are provided to sustain the acquired key outcomes.

Stability and bifurcation analysis for a fractional-order cancer model with two delays

Considering that healthy tissue cells and tumor cells restrain each other’s the average growth rate with a corresponding delay, a fractional-order cancer model with time delays is established. Firstly, by selecting different delays as bifurcation parameters, the delay-independent stability and Hopf bifurcation conditions of such system are derived. Then, some interesting dynamical phenomena of the system under different initial values can be observed, such as a pair of coexisted stable periodic solution, equilibrium point transition, and even chaos. Finally, some numerical simulations are exhibited to substantiate the obtained results. The work reveals that the fractional order and delays play an important role in the stability behavior and bifurcation characteristics of the system, and that a suitable control strategy of the system can be designed by selecting reasonable system parameters (fractional orders and time delays).

Asymptotic stabilisation of coupled delayed time fractional reaction diffusion systems with boundary input disturbances via backstepping sliding-mode control

In this paper we study the asymptotic stabilisation for coupled time fractional reaction diffusion (FRD) systems with time varying delays and input disturbances by backstepping-based boundary sliding-mode control. Here, the spatially varying diffusion coefficients can be same or distinct. To stabilise the system, we first use an invertible backstepping transformation to convert an original dynamics into a target dynamics with new manipulable inputs and perturbations. Then, we employ the sliding-mode algorithm to design this discontinuous controller to suppress disturbances. In this case, we obtain the combined backstepping/sliding-mode controller of the original dynamics. By using the fractional Halanay's inequality, the delay-independent stability condition is obtained for the asymptotic stabilisation of the delayed target system and therefore of the delayed original system under the combined controller. Fractional numerical examples are given to verify the efficiency of the proposed synthesis.

Washout filter control technique for a fractional-order chaotic finance model

On the basis of the previous publications, we set up a new fractional-order chaotic finance model. Taking advantage of washout filter controller, we are committed to the study on the chaotic control for the considered fractional-order chaotic finance model. Applying the stability criterion and Hopf bifurcation knowledge of fractional order differential dynamical system, a series of delay-independent stability and bifurcation conditions are established to assure the stability and the occurrence of Hopf bifurcation of the fractional-order controlled chaotic finance model. The investigation indicates that the role of delay in controlling the stability and Hopf bifurcation for the fractional-order controlled chaotic finance model is fully reflected. In the end, numerical simulation figures and bifurcation plots are presented to sustain the established primary conclusions. Our work supplements the earlier studies and enriches the chaos control theory of fractional-order dynamical system.

Observer-based state estimation for memristive neural networks with time-varying delay

This paper investigates the observer-based state estimation of memristive neural networks (MNNs) with time-varying delay. In order to obtain the accurate state information of the switching MNNs system, a new full-order state observer based on system measurement output is developed such that the reconstruction of states is achieved. By applying set-valued maps and differential inclusions, some sufficient conditions for delay-independent and delay-dependent asymptotic stability are obtained. The validity of theoretical results is verified via numerical examples.

Theoretical analysis and computer simulations of a fractional order bank data model incorporating two unequal time delays

In order to reveal the change law of bank data and manage bank effectively, building mathematical models is a very effective approach. In this present study, we set up a novel fractional-order bank data model incorporating two unequal time delays. Firstly, we discuss the existence and uniqueness, non-negativeness, boundedness of the solution to the established bank data model by virtue of contraction mapping theorem, mathematical analysis technique, construct of an appropriate function, respectively. Secondly, the stability and the creation of Hopf bifurcation are investigated via the stability criterion and bifurcation principle of fractional-order differential equation, five new delay-independent stability conditions and bifurcation criteria ensuring the stability behavior and the onset of Hopf bifurcation of the involved bank data model are established. Furthermore, the role of time delay in stabilizing system and controlling the generation of Hopf bifurcation is sufficiently displayed. Thirdly, the global stability of the considered fractional-order bank data model is systematically explored. Fourthly, the Hopf bifurcation control issue of fractional-order bank data model is studied via PDξ controller. Finally, computer simulations are executed to verify the established primary results. The derived conclusions of this study are absolutely innovative and possess important theoretical guiding significance in maintaining a good operation of banks.

Chaos Control for a Fractional-Order Jerk System via Time Delay Feedback Controller and Mixed Controller

In this study, we propose a novel fractional-order Jerk system. Experiments show that, under some suitable parameters, the fractional-order Jerk system displays a chaotic phenomenon. In order to suppress the chaotic behavior of the fractional-order Jerk system, we design two control strategies. Firstly, we design an appropriate time delay feedback controller to suppress the chaos of the fractional-order Jerk system. The delay-independent stability and bifurcation conditions are established. Secondly, we design a suitable mixed controller, which includes a time delay feedback controller and a fractional-order PDσ controller, to eliminate the chaos of the fractional-order Jerk system. The sufficient condition ensuring the stability and the creation of Hopf bifurcation for the fractional-order controlled Jerk system is derived. Finally, computer simulations are executed to verify the feasibility of the designed controllers. The derived results of this study are absolutely new and possess potential application value in controlling chaos in physics. Moreover, the research approach also enriches the chaos control theory of fractional-order dynamical system.

Stability Analysis and Robust Stabilization of Uncertain Fuzzy Time-Delay Systems

New sufficient conditions for delay-independent and delay-dependent robust stability of uncertain fuzzy time-delay systems based on uncertain fuzzy Takagi-Sugeno (T-S) models are presented by using the properties of matrix and norm measurements. Further sufficient conditions are formulated, in terms of the linear matrix inequalities (LMIs) of robust stabilization, and are developed via the technique of parallel distributed compensation (PDC), and then the simplification of the conditions for the controller design of uncertain fuzzy time-delay systems. The proposed methods are simple and effective. Some examples below are presented to illustrate our results.

Parametric Stabilization of the Ring and Linear Neural Network with Two Delays

This paper is devoted to the problem of stabilizing a Hopfield-type neural network with bi-directional ring architecture and two delays. The delay-independent and delay-dependent stability conditions are explicitly presented by the method of the characteristic roots and the skill of mathematical analysis. Moreover, if a link between the adjacent two neurons is cut, the ring neural network turns to a linear one, and the stability results are also established. Furthermore, a comparative analysis for the ring and linear network shows that the stability domain is enlarged after the breaking.

Stability analysis and synthesis of stabilizing controls for a class of nonlinear mechanical systems

This paper is concerned with the problems of stability and stabilization for a class of nonlinear mechanical systems. It is assumed that considered systems are under the action of linear gyroscopic forces, nonlinear homogeneous positional forces and nonlinear homogeneous dissipative forces of positional–viscous friction. An approach to strict Lyapunov functions construction for such systems is proposed. With the aid of these functions, sufficient conditions of the asymptotic stability and estimates of the convergence rate of solutions are found. Moreover, systems with delay in the positional forces are studied, and new delay-independent stability conditions are derived. The obtained results are used for developing new approaches to the synthesis of stabilizing controls with delay in feedback law.

Static output feedback control of positive linear systems with output time delays

ABSTRACTIn this paper, we discuss a new problem of static output feedback controllers design for positive systems with delayed output measurements. When delayed output measurements are exclusively used as feedback control signals, previous control design methods for positive systems relying on the so-called delay-independent positivity and stability conditions are unable to synthesise a stable static output feedback controller for positive systems. A new method based on delay-dependent positivity and stability conditions is proposed in this paper to tackle this issue. We show that the synthesis of static output feedback controllers for positive systems under the effect of delayed output measurements is feasible under the newly proposed design method. Numerical examples are given to demonstrate the effectiveness of the new result.

Delay-tolerant distributed voltage control for multiple smart loads in AC microgrids

With increasing penetration of variable loads and intermittent distributed energy resources (DERs) with uncertainty and variability in distribution systems, the power system gradually inherits some features (e.g., lack of rotating inertia), which leads to the voltage instability in microgrids. As a means to provide stability support for smart grid against high penetration of intermittent DERs, inverter-based smart loads across the distribution grid has been suggested recently. Accordingly, this paper presents a delay-tolerant distributed voltage control scheme based on consensus protocol for multiple-cooperative smart loads through effective demand-side management in ac microgrids, in which the time-delay effect on transmission communication occurred in information exchanges is considered. The proposed distributed voltage control scheme always enables the output voltage of each smart load to be synchronized to their reference value, which improves the robustness of system stability against transmission communication delays. The Lyapunov–Krasovskii functions are employed to analyze the stability of our proposed distributed control scheme, then the delay-independent stability conditions are derived, which allows some large communication delays. Moreover, the sensitivity analysis is developed to show how the time delay affects system dynamics in order to validate the robustness of proposed delay-independent stability conditions. Furthermore, a sparse communication network is employed to implement the proposed distributed control protocols, which thus satisfies the plug-and-play requirement of smart microgrids. Finally, the simulation results of an ac microgrid in MATLAB/SimPowerSystems are presented to demonstrate the effectiveness of the proposed control methodology.

Lyapunov Stability of the Generalized Stochastic Pantograph Equation

The purpose of the paper is to study stability properties of the generalized stochastic pantograph equation, the main feature of which is the presence of unbounded delay functions. This makes the stability analysis rather different from the classical one. Our approach consists in linking different kinds of stochastic Lyapunov stability to specially chosen functional spaces. To prove stability, we check that the solutions of the equation belong to a suitable space of stochastic processes, instead of searching for an appropriate Lyapunov functional. This gives us possibilities to study moment stability, stability with probability 1, and many other stability properties in an efficient way. We show by examples how this approach works in practice, putting emphasis on delay-independent stability conditions for the generalized stochastic pantograph equation. The framework can be applied to any stochastic functional differential equation with finite dimensional initial conditions.

Stability and bifurcation of delayed bidirectional gene regulatory networks with negative feedback loops

This paper studies the stability and bifurcation of three cases of bidirectional gene regulatory networks with negative feedback loops and time delays. The uniqueness of the positive equilibrium point of the gene regulatory networks is verified. The delay independent stability conditions of the networks are established by analyzing their corresponding characteristic equations. The existence of the Hopf bifurcation of the networks with or without time delays is presented. Numerical simulations demonstrate the correctness of the obtained theoretical results.

Delay-independent stability conditions for a class of nonlinear difference systems

The paper addresses the asymptotic stability problem for a class of difference systems with nonlinearities of a sector type and time-delay. A new approach to Lyapunov–Krasovskii functionals constructing for considered systems is proposed. On the basis of the approach, delay-independent asymptotic stability conditions and estimates of the convergence rate of solutions are derived. In addition, stability of perturbed systems is investigated in the case where nonstationary perturbations admit zero mean values. Some examples are given to illustrate the obtained results.

Exponential Stability of Two-Dimensional Homogeneous Monotone Systems With Bounded Directional Delays

One-dimensional (1-D) monotone systems have received considerable attention recently due to their wide applicability and interesting mathematical properties. One of these special properties is that, for LTI monotone systems, exponential stability is insensitive to time-delays. Some extensions to 1-D nonlinear monotone systems based on conditions of homogeneity have also been reported. In this paper, we study the problem of exponential stability of discrete-time 2-D nonlinear monotone systems described by the Roesser model with time-varying delays. Specifically, based on the monotone property and homogeneity of the associated vector fields, necessary and sufficient delay-independent exponential stability conditions are derived. The magnitudes of delays are also taken into deriving an explicit estimation of the exponential decay rate which correlates the impact of delays on the system performance. Two examples are given to demonstrate the effectiveness of the obtained results.

Global stability for a class of functional differential equations (Application to Nicholson's blowflies and Mackey-Glass models)

Global asymptotic and exponential stability of equilibria for the following class of functional differential equations with distributed delay is investigated\begin{document}$ x'(t)=-f(x(t))+\int_{0}^{\tau}h(a)g(x(t-a))da.$\end{document}We make our analysis by introducing a new approach, combining a Lyapunov functional and monotone semiflow theory. The relevance of our results is illustrated by studying the well-known integro-differential Nicholson's blowflies and Mackey-Glass equations, where some delay independent stability conditions are provided. Furthermore, new results related to exponential stability region of the positive equilibrium for these both models are established.