Exponential Stability Criteria Research Articles

Approximations in Mean Square Analysis of Stochastically Forced Equilibria for Nonlinear Dynamical Systems

Motivated by important applications to the analysis of complex noise-induced phenomena, we consider a problem of the constructive description of randomly forced equilibria for nonlinear systems with multiplicative noise. Using the apparatus of the first approximation systems, we construct an approximation of mean square deviations that explicitly takes into account the presence of multiplicative noises, depending on the current system state. A spectral criterion of existence and exponential stability of the stationary second moments for the solution of the first approximation system is presented. For mean square deviation, we derive an expansion in powers of the small parameter of noise intensity. Based on this theory, we derive a new, more accurate approximation of mean square deviations in a general nonlinear system with multiplicative noises. This approximation is compared with the widely used approximation based on the stochastic sensitivity technique. The general mathematical results are illustrated with examples of the model of climate dynamics and the van der Pol oscillator with hard excitement.

Novel criteria for exponential stability in mean square of stochastic delay differential equations with Markovian switching

Novel criteria for exponential stability in mean square of stochastic delay differential equations with Markovian switching

Almost Sure Stability of Complex-Valued Complex Networks: A Noise-Based Delayed Coupling Under Random Denial-of-Service Attacks.

This article is concerned with stability for stochastic complex-valued delayed complex networks under random denial-of-service (RDoS) attacks. Different from the existing literature on the stability of stochastic complex-valued systems that concentrate on moment stability, we investigate almost sure stability (ASS), where noise plays a stabilizing role. It is noted that, besides the vertex systems influenced by noise, the interactions among vertices are also at the mercy of noise. As a consequence, an innovative noise-based delayed coupling (NDC) in the presence of RDoS attacks is proposed first to accomplish the stability of complex-valued networks, where the RDoS attacks have a certain probability of triumphantly interfering with communications at active intervals of attackers. Namely, RDoS attacks considered are randomly launched at active periods, which is more realistic. In terms of the Lyapunov method and stochastic analysis theory, an almost sure exponential stability (ASES) criterion of the system discussed straightforwardly is developed by constructing a delay-free auxiliary system, while removing the traditional assumption of moment stability. The criterion strongly linked with topological structure, RDoS frequency, attack successful probability, and noise intensity reveals that the higher the noise intensity, the faster the convergence rate is for the stability of the network. In light of the criterion established, we present an algorithm that can be employed to analyze the tolerable attack parameters and the upper bound of the coupling delays, under the prerequisite of guaranteeing the stability of the network. Eventually, the theoretical results are applied to inertial complex-valued neural networks (ICNNs) and an illustrative example is presented to substantiate the efficiency of the theoretical works.

Exponential stability of impulsive random delayed nonlinear systems with average-delay impulses

In this paper, we investigate the pth moment exponential stability of impulsive random delayed nonlinear systems (RDNS) with average-delay impulses. Utilizing the average impulsive interval, average impulsive delay, and the Lyapunov method, we present several criteria for pth exponential stability in these systems under a novel condition, diverging from previous literature. Additionally, we explore the effects of delayed impulses, analyzing both destabilizing and stabilizing impulses. Our findings reveal the dual effects of time delay in impulses, which can potentially destabilize a stable system or stabilize an unstable one.

Exponential stability of delayed discrete‐time systems with averaged delayed impulses

AbstractThis article investigates the exponential stability of nonlinear discrete‐time systems with time‐varying state delay and delayed impulses, where the delays in impulses are not fixed. Specifically, the study is separated into two cases: (1) stability of delayed discrete‐time systems with destabilizing delayed impulses, where the time delays in impulses can be flexible and even larger than the length of the impulsive interval; (2) stability of delayed discrete‐time systems with mixed delayed impulses (means stabilizing and destabilizing delayed impulses exist simultaneously), where the time delays in impulses are unfixed between two adjacent impulsive instants. First, the concept of average impulsive delay (AID) is extended to discrete‐time systems with delayed impulses. Then, some Lyapunov‐based exponential stability criteria are provided for delayed discrete‐time systems with delayed impulses, where the impulses satisfy the average impulsive interval (AII) condition and the delays in impulses satisfy the AID condition. For the delayed discrete‐time systems with mixed delayed impulses, the exponential stability criterion is provided by limiting the geometric average of the impulses' strengths. The obtained results can be used to study the delayed discrete‐time systems with some large impulses which may even be unbounded. It's also shown that the delays in impulses can have a stabilizing effect on the stability of delayed discrete‐time systems. Some numerical examples are also provided to illustrate the effectiveness and advantage of the theoretical results.

Novel Exponential Stability Criteria for Switched Neutral-Type Neural Networks With Mixed Delays

Novel Exponential Stability Criteria for Switched Neutral-Type Neural Networks With Mixed Delays

New Criteria for Robust Exponential Stability of Uncertain Discrete-Time Switched Systems with Time-Varying Delay via Average Dwell Time Approach and Under Arbitrary Switching Signal

New Criteria for Robust Exponential Stability of Uncertain Discrete-Time Switched Systems with Time-Varying Delay via Average Dwell Time Approach and Under Arbitrary Switching Signal

Exponential Stabilization of Semi-Markov Reaction-Diffusion Memristive NNs via Event-Based Spatially Pointwise-Piecewise Switching Control.

This article considers both the semi-Markov jumping phenomenon and spatial distribution characteristics when investigating the exponential stabilization of memristive neural networks (MNNs). The introduction of the semi-Markov jumping parameters relaxes the restriction on the sojourn time of Markovian MNNs. To increase the operability while ensuring control effect, a novel event-based spatially pointwise-piecewise switching control scheme is presented under a unified spatial division criterion, in which the pointwise and piecewise control can switch according to the preset event condition for the applicability to different control requirements. Moreover, by constructing a semi-Markov Lyapunov functional and utilizing the properties of the considered cumulative distribution function, the final exponential stabilization criterion and two related corollaries are obtained. Finally, simulation results illustrate the effectiveness and superiority of the proposed control strategy.

Stability of Delayed Homogeneous Positive Differential–Difference Systems

Stability theory of linear differential-difference system has been well-established, while fewer results can be found for nonlinear differential-difference systems. In this paper, stability and boundedness of homogeneous differential-difference system with bounded delay is studied based on the system positivity. At first, an exponential stability criterion is obtained, which is an extension of an existing result. Next, another boundary is computed under the previous condition, which proves to be tighter than the first result at least in some cases. Then a finite-time stability condition is achieved for the delay-free system, and an upper bound of the settling time and an explicit boundary of the state are derived. Finally, a numerical example is given to verify the results presented in this paper.

Intermittent Sampled-Data Control for Local Stabilization of Neural Networks Subject to Actuator Saturation: A Work-Interval-Dependent Functional Approach.

This article is concerned with the local stabilization of neural networks (NNs) under intermittent sampled-data control (ISC) subject to actuator saturation. The issue is presented for two reasons: 1) the control input and the network bandwidth are always limited in practical engineering applications and 2) the existing analysis methods cannot handle the effect of the saturation nonlinearity and the ISC simultaneously. To overcome these difficulties, a work-interval-dependent Lyapunov functional is developed for the resulting closed-loop system, which is piecewise-defined, time-dependent, and also continuous. The main advantage of the proposed functional is that the information over the work interval is utilized. Based on the developed Lyapunov functional, the constraints on the basin of attraction (BoA) and the Lyapunov matrices are dropped. Then, using the generalized sector condition and the Lyapunov stability theory, two sufficient criteria for local exponential stability of the closed-loop system are developed. Moreover, two optimization strategies are put forward with the aim of enlarging the BoA and minimizing the actuator cost. Finally, two numerical examples are provided to exemplify the feasibility and reliability of the derived theoretical results.

Novel Criteria for Exponential Stability of Neutral Functional Differential Equations

We address the challenging problem of exponential stability of general neutral functional differential equations. By a novel approach, we present some new explicit criteria for the exponential stability of neutral functional differential equations. Some remarks and illustrative examples are given.

Impulsive Stability for Positive Linear Differential-Algebraic Equations With Time-Varying Delay

This paper deals with the impulsive stability problem for positive linear differential-algebraic equations (DAEs) with a time-varying delay. First, a sufficient condition for the positivity of the considered system is addressed. Then, a new exponential stability criterion for positive linear DAEs with a time-varying delay is obtained based on a suitable change of variables. According to our results, a stable impulse-free system can keep its original stability property under certain destabilizing impulsive perturbations. It should be noted that it is the first time the exponential stability results for impulsive positive linear DAEs are given. For this purpose, delay-range dependent sufficient conditions for such systems are stated in the paper. An additional numerical example is provided to demonstrate the results' efficacy.

Exponential Stability for Second-Order Neutral Stochastic Systems Involving Impulses and State-Dependent Delay

Exponential stability criteria for neutral second-order stochastic systems involving impulses and state-dependent delay have been addressed in this paper based on stability theory, stochastic analysis, and the inequality technique. Some sufficient conditions are given to establish the exponential stability of such systems, which is well-established in the deterministic case, but less known for the stochastic case. In our model, the noise effect can be described as a symmetric Wiener process. By formulating the impulsive integral technique, exponential stability analysis of the pth moment of the second-order system involving stochastic perturbation is established. As an application that illustrates the theoretical formulation, an example is presented.

Event-triggered control design with varying gains for polynomial fuzzy systems against DoS attacks

This paper presents an innovative event-triggered control scheme for addressing the stabilization problem of polynomial fuzzy systems under the influence of Denial-of-Service (DoS) attacks. The proposed controller utilizes a sampling-based event-triggered mechanism to reduce communication resources and avoid Zeno behavior. Furthermore, a novel polynomial fuzzy model-based control system is developed to investigate the impact of periodic DoS attacks and the addressed event-triggered mechanism on system stability. To improve system performance, control gains are updated at each triggering instant. The exponential stability criteria are formulated in the form of sum-of-square constraints, supported by a triggering instant dependent piecewise Lyapunov-Krasovskii functional and an online asynchronous premise reconstruction approach. Finally, the efficiency and usefulness of the theoretical findings are validated through simulation examples.

Global robust exponential stability of interval BAM neural networks with multiple time-varying delays: A direct method based on system solutions

This paper analyzes global robust exponential stability of interval bidirectional associative memory (BAM) neural networks with multiple time-varying delays, proposes a direct method based on system solutions, and gives sufficient conditions under which interval BAM neural networks have a unique and globally robustly exponentially stable equilibrium point. This method not only avoids the difficult to set up any Lyapunov–Krasovskii functional, but also derives simpler global robust exponential stability criteria. Compared with the data from other literature, the robust exponential stability criteria obtained in this paper have been presented to have more merits theoretically and numerically.

Adaptive event-triggered PID load frequency control for multi-area interconnected wind power systems under aperiodic DoS attacks

In this article, an adaptive event-triggered proportional–integral–derivative (PID) load frequency control (LFC) strategy is designed for multi-area interconnected wind power systems under aperiodic denial-of-service (DoS) attacks. First, to relieve the frequency fluctuation caused by wind power integration, a dynamic model including the doubly-fed induction generator is established for multi-area interconnected wind power systems. Second, to avoid superfluous occupation of network communication bandwidth, an adaptive event-triggered mechanism with memory property is proposed under aperiodic DoS attacks. Then, with the aid of intermittent control method, a memory-based PID LFC strategy is achieved to stabilize the frequency of wind power systems. Third, by constructing a switched Lyapunov-Krasovskii functional, two exponential stability criteria meeting the H∞ norm bound are derived. Finally, simulation examples are provided to verify the effectiveness of the presented control strategy.

Resilient Event-Triggered Load Frequency Control for Cyber-Physical Power Systems Under DoS Attacks

In cyber-physical power systems (CPPSs), additional control as the compensating control plays a very important part in load frequency control (LFC) systems. The additional control in the LFC system is constrained by limited communication resources and cyber-attacks, which may cause performance degradation or destabilize the system. Accordingly, this paper proposes resilient event-triggered LFC for CPPSs with an additional control loop under denial-of-service (DoS) attacks. Firstly, a resilient event-triggered communication scheme is presented to reduce the occupation of communication resources under DoS attacks in the additional control loop. Then, different from existing event-triggered LFC systems, this paper establishes a novel switched LFC system model, where the resilient event generator is integrated into an additional control loop when suffering from DoS attacks. It is the first time that the additional control loop of the LFC system simultaneously considers communication resources and cyber-security. Furthermore, we derive exponential stabilization criteria by applying the Lyapunov stability theory based on the established model. Criteria are derived to obtain the weighting matrix and controller gain simultaneously by applying the linear matrix inequality technique. Finally, a one-area and two multi-area CPPSs with the additional control loop under DoS attacks are used to testify the availability of the proposed resilient event-triggered LFC scheme.

Resilient adaptive event‐triggered synchronization control of piecewise‐homogeneous Markov jump delayed neural networks under aperiodic DoS attacks

SummaryUnder the aperiodic Denial‐of‐service (DoS) attacks, this paper studies the resilient adaptive event‐triggered synchronization control problem for a class of Piecewise‐Homogeneous Uncertain Markov Jump Neural Networks (PHUMJNNs) with time‐varying delays. First of all, a new way of carving DoS attacks is given from the defenders' perspective, that is, aperiodic DoS attacks based on fixed detection periods. Then, under such attacks, a new Resilient Adaptive Event‐triggered Communication (RAETC) is designed between sensor and controller, which has a threshold function based on the net change rate and is real‐time updated depending on the present sampling state. Next, a single functional is used in the construction of the Lyapunov‐Krasovskii functional, while a new looped functional is introduced that makes full use of the state information of the current instant , the trigger instant and the next trigger instant . Based on the constructed single functional, under the framework of the input delay method and the linear matrix inequality technique, the exponential mean square stabilization criterion of the error system is obtained, which makes the master system and the slave system synchronized. In the end, three simulation examples are used to illustrate the validity of the obtained results.

Absolute Exponential Stability Criteria for Some Classes of Nonlinear Time-Varying Systems with Delays and Sector Nonlinearities

Absolute Exponential Stability Criteria for Some Classes of Nonlinear Time-Varying Systems with Delays and Sector Nonlinearities

Adaptive event-triggered control for stability of fractional-order T-S fuzzy multi-links complex networks with random coupling delay

The main concern of this article is to address the exponential stability problem of fractional-order T-S fuzzy multi-links complex networks through designing the novel intermittent adaptive event-triggered control (IAE-TC) scheme. To reduce unnecessary transmission burden as much as possible in an allowable range, dynamic variable is introduced into fuzzy intermittent adaptive control and then fuzzy intermittent adaptive event-triggered control is established. In this control scheme, the controller is only activated when the event triggering conditions are not met, and has adaptability to the evolution results of the controlled network. Furthermore, by applying the Lyapunov method, the graph theory and the IAE-TC strategy, exponential stability criteria of the proposed networks are deduced. Meanwhile, we prove that Zeno behavior does not exist. Ultimately, an application about fractional-order T-S fuzzy multi-links competitive neural networks model is given to demonstrate the validity of the results, simultaneously, we show some numerical simulations.