Exponential Stability Research Articles

Reachable Set Estimation of Multiagent Systems: An Approximate Consensus Perspective

This paper is concerned with the estimation of reachable set for leaderless multi-agent systems (MASs) under fixed topology with bounded disturbances and nonzero initial conditions. In-neighbors' information is collected to design the protocol such that all agents' state trajectories are constrained within a compact set, and asymptotic consistency is regulated for disturbance-free MASs in the exponential stability sense while approximate consistency is regulated for noise-disturbed MASs in the input-to-state stability sense. The agreement dynamics are characterized by the consensus function with determined initial condition, whose estimated reachable set has non-empty intersection with that of MAS. The analytical framework is also applied to Markovian topology switching subject to completely and partially known transition rates, respectively. Numerical simulations confirm the theoretical results.

Hybrid event-triggered control for networked switched Takagi–Sugeno fuzzy systems with aperiodic DoS attacks

This article investigates the event-triggered control problem for networked switched Takagi–Sugeno fuzzy systems (NSTSFSs) with denial of service (DoS) attacks. First, an attack-instant-constrained hybrid event-triggered mechanism (ETM) is proposed, which uses the acknowledgment character (ACK) detection scheme. It can describe the triggering schemes under different attack intervals and modify the triggering frequency based on the performance of the system. Second, a new segmented Lyapunov function is designed that takes into account the asynchronous behavior of system and controller modes, as well as DoS frequency and duration constraints. Then, sufficient conditions are provided to ensure the exponential stability of the system and have an H∞ performance. Furthermore, a collaborative design scheme is proposed to obtain controller gains, the switching law, and event-triggered parameters. Finally, the accuracy and effectiveness of this method are verified through two simulation examples.

Is exponential stability achievable in singular perturbed delayed systems with time-varying parameters? A comprehensive analysis

The present article conducts an investigation into the phenomenon of exponential stability within singular perturbed delayed systems, incorporating time-varying parameters. Singularly perturbed systems serve as essential tools in modeling intricate systems characterized by multiple time scales, wherein one subsystem exhibits significantly faster evolution than the others. The presence of small delays introduces complexities, influencing both state derivatives and delays, further accentuating the intricacies of the system. Drawing upon the principles of singular perturbation theory, the article introduces a novel approach to analyzing the stability of these complex systems, eschewing the conventional assumption of exponential stability in the fast subsystem. Within the scope of this study, we propose a rigorous stability analysis, utilizing Linear Matrix Inequality (LMI) methods, while considering time-varying parameters that exert substantial influence on the system's dynamics. The proposed methodology enables the exploration of system stability beyond conventional assumptions, imparting valuable insights into the behavior of singular perturbed delayed systems amidst varying conditions. Through extensive numerical simulations, the effectiveness and robustness of the approach are validated, illuminating the stability properties of these intricate systems. Comparative studies with existing techniques, which assume exponential stability in the fast subsystem, demonstrate the distinct advantages and uniqueness of the presented approach. The findings underscore the significance of accounting for time-varying parameters in achieving a comprehensive understanding of the exponential stability inherent in singular perturbed delayed systems. This research makes substantial contributions to the field of system stability analysis, particularly in the context of singular perturbed delayed systems featuring time-varying parameters. The originality of our approach lies in introducing a comprehensive analysis framework that overcomes the limitations of existing methodologies. By integrating a novel stability analysis method based on Linear Matrix Inequalities (LMIs), we offer a fresh perspective on achieving exponential stability in such complex systems. Significantly, our work addresses a critical gap in current literature by challenging the assumption of exponential stability in the fast subsystem, a key feature of singularly perturbed systems. Through a meticulous examination of time-varying parameters, we unveil their profound impact on system dynamics, thus enriching the understanding of stability behaviors. The potential real-world applications of our findings span diverse fields, ranging from engineering to mathematical modeling. Performance metrics are a key focal point of our research. Numerical simulations employing our proposed LMIs serve as a robust benchmark, demonstrating the superior stability achieved in comparison to existing methods. This performance-driven evaluation ensures the practical applicability and reliability of our analysis approach across various scenarios.

Predictor-Based Decentralized Event-Triggered Secure Control for Nonlinear Cyber-Physical Systems Under Replay Attacks and Time Delay

This paper investigates the problem of predictor-based decentralized event-triggered secure control for nonlinear cyber-physical systems (CPSs) subject to replay attacks and time delay. To overcome the limitation of the network bandwidth, a periodic decentralized event-triggered scheme (PDETS) is designed for non-strict feedback nonlinear CPSs in the presence of replay attacks. Then, decentralized output feedback controllers are constructed by designing predictor-based observers to attenuate the influences of replay attacks and time delay. Based on the proposed new framework, the global exponential stability (GES) of the resulting nonlinear CPSs can be guaranteed. Finally, two application examples verify the effectiveness of the proposed method.

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

Model robustness for feedback stabilization of open quantum systems

This paper builds upon and expands the findings presented in Liang et al. (2021). Our focus lies in scenarios where initial states and model parameters remain unknown. In contrast to prior research, we consider multiple measurement channels, addressing the challenge of global exponential stabilization towards a chosen target subspace. Under quantum non-demolition conditions, our analysis establishes essential tools for achieving feedback stabilization. Furthermore, we explore the utilization of a simplified filter as a viable alternative to full state estimator. While the effectiveness of this simplified filter was numerically examined in Cardona et al. (2020), our paper offers a comprehensive proof of its applicability in feedback stabilization. Furthermore, our analysis may serve as an inspiration for demonstrating the validation of the robust feedback stabilization through generic approximate filters.

Robust stability of moving horizon estimation for continuous-time systems

Abstract We consider a moving horizon estimation (MHE) scheme involving a discounted least squares objective for general nonlinear continuous-time systems. Provided that the system is detectable (incrementally integral input/output-to-state stable, i-iIOSS), we show that there exists a sufficiently long estimation horizon that guarantees robust global exponential stability of the estimation error in a time-discounted L 2-to-L ∞ sense. In addition, we show that i-iIOSS Lyapunov functions can be efficiently constructed by verifying certain linear matrix inequality conditions. In combination, we propose a flexible Lyapunov-based MHE framework in continuous time, which particularly offers more tuning possibilities than its discrete-time analog, and provide sufficient conditions for stability that can be easily verified in practice. Our results are illustrated by a numerical example.

Explicit convergence relations for a class of discrete LTV systems and its application to performance analysis of deterministic learning

A class of linear time-varying (LTV) systems commonly appears in classical adaptive control and identification, in which the accurate identification of parameters is highly related to their exponential stability. However, there is limited research on explicit convergence relations for discrete LTV systems. In this article, the explicit convergence relation of a class of discrete LTV systems is first established, in which strict Lyapunov functions are constructed by considering the convergence properties of the interconnected unforced subsystems. Next, based on the derived explicit convergence relation, a performance analysis of deterministic learning under the sampling-data framework is established. We show that the learning speed and learning accuracy increase with the persistent excitation (PE) level and decrease with the identifier gain. Moreover, an optimal learning gain exists related to the identifier gains. To illustrate the results, simulation studies are included.

Decentralized Predictor Stabilization for Interconnected Networked Control Systems with Large Uncertain Delays and Event-Triggered Input

In this article, we propose a control scheme with predictors in a decentralized manner for coupled networked control systems (NCSs) under uncertain, large time-delays and event-triggered inputs. The network-induced delays are handled via the prediction; thus, the delay value is allowed to be large, and the burden of the network is relieved by the event-triggered input. Two methods are employed to deal with the large delay issue: the state and output feedback. When the state of each subsystem is measurable, full-state feedback is used, whereas when the plant state cannot be measured, output feedback is employed with the help of an observer, which is more common in practice. Instead of treating the interactive plants like a global system, the exponential stability of the coupled systems, under decentralized predictors with asynchronous sampled-data feedback, is analyzed in a decentralized way. Finally, the proposed methods are verified via an example of three interconnected cart–pendulum systems, while such systems would not be stabilizable by the traditional approach when the network-induced delays are relatively large.

Global exponential stability of quaternion bidirectional associative memory neural networks with multiple delays

In this paper, the global exponential stability of quaternion BAM neural networks with mixed delays is investigated. The involved delays include multiple time‐varying transmission delays and unbounded distributed delays. Existence and uniqueness of equilibrium point of the considered neural networks are investigated by using the homeomorphism theory between topology spaces. To show sufficient conditions for global exponential stability of the unique equilibrium point, a method based on estimation of solutions is presented. The acquired stability conditions contain only several simple linear scalar inequalities, which can be easily solved. The availability of theoretical results is shown by a numerical example. A point worth emphasizing is that the method based on estimation of solutions is applicable for models of many time‐delay systems after a minor modification.

Exponential Stabilization of a Flexible Structure: A Delayed Boundary Force Control Versus a Delayed Boundary Moment Control

Exponential Stabilization of a Flexible Structure: A Delayed Boundary Force Control Versus a Delayed Boundary Moment Control

Almost sure exponential stabilization of impulsive Markov switching systems via discrete-time stochastic feedback control

It is well known that noise can stabilize an unstable Markov switching system (MSS). However, given an unstable impulsive Markov switching system (IMSS), can it be stabilized by noise? To the best of the author’s knowledge, this question has been rarely explored. If the stochastic feedback controller is observed in discrete time, the research is more difficult. In this paper, a comparative method is used to establish a noise stabilization strategy based on discrete-time state and mode observations for IMSSs. In addition, we use the stationary distribution of the ergodic Markov chain instead of the M-matrix technique to obtain the pth moment estimation on the gap between the discrete-time observed controlled system’s states and the auxiliary system’s states, so that the control strategy can be applied to a wider class of IMSSs. Finally, we applied the proposed control scheme to impulsive neural networks with Markovian switching (INNs-MS) and impulsive boost converter systems (IBCSs). Through an example and several simulations, we validated the effectiveness and feasibility of this control scheme.

Global exponential convergence and synchronization for exponential numerical competitive neural networks with different time scales and fuzzy logic

For nonlocal fuzzy delayed competitive neural networks, a novel difference model is first developed in this article using the Mittag-Leffler Euler difference method. Secondly, the existence of a sole globally bounded solution and globally exponential stability to the discrete-time networks are addressed based on Banach contractive mapping principle and the constant variation formula for sequences. Besides, exponential synchronization of the discrete-time networks is investigated and a feedback controller is designed from the viewpoint of the theory of controls. It is the first time to consider nonlocal fuzzy delayed competitive neural networks by using Mittag-Leffler Euler differences. In contrast to nonlocal discrete approaches, such difference competitive neural networks could preferably figure the features of continuous networks. The difference method in this paper extends and improves the traditional difference approaches, for example, Adams-Bashforth Euler differences. Moreover, this article explores some avenue for the research of discrete-time fractional-order systems and develops a set of theories and methodologies for the future investigations.

Exponential Stability of Stochastic Time-Delay Neural Networks with Random Delayed Impulses

The mean square exponential stability of stochastic time-delay neural networks (STDNNs) with random delayed impulses (RDIs) is addressed in this paper. Focusing on the variable delays in impulses, the notion of average random delay is adopted to consider these delays as a whole, and the stability criterion of STDNNs with RDIs is developed by using stochastic analysis idea and the Lyapunov method. Taking into account the impulsive effect, interference function and stabilization function of delayed impulses are explored independently. The results demonstrate that delayed impulses with random properties take a crucial role in dynamics of STDNNs, not only making stable STDNNs unstable, but also stabilizing unstable STDNNs. Our conclusions, specifically, allow for delays in both impulsive dynamics and continuous subsystems that surpass length of impulsive interval, which alleviates certain severe limitations, such as presence of upper bound for impulsive delays or requirement that impulsive delays can only exist between two impulsive events. Finally, feasibility of the theoretical results is verified through three simulation examples.

Secure memory adaptive event‐triggered filter design of nonlinear network system under hybrid network attacks with application to tunnel diode circuit

AbstractThis article investigates the problem of secure memory adaptive event‐triggered filter design for nonlinear network systems under hybrid network attacks. First, the introduction of memory adaptive event‐triggered mechanism and numerical quantization is employed to enhance system performance, optimize network channel utilization, and prevent network congestion. Second, we consider the impact of deceptive attacks and DoS attacks occurring in the network channel on data transmission, which form the hybrid network attacks studied in this article. Subsequently, based on the established error model, we derive sufficient conditions for the mean‐square exponential stability of the system under a given performance index using Lyapunov–Krasovskii function and linear matrix inequality (LMI) techniques. Furthermore, the filter parameters are determined using the LMI method. Finally, we illustrate the feasibility and generality of the conclusions through numerical simulation examples and a tunnel diode circuit system.

Asynchronous H∞ output tracking control for uncertain networked switched systems with mode-dependent average dwell time: an event-driven mechanism

This paper considers the problem of event-triggered H ∞ output tracking control for uncertain networked switched systems with both communication constraints and asynchronous switching. A new sampled delay-dependent error tracking uncertain networked switched system is constructed on the basis of event-triggered communication mechanism (ETCM) and the given reference model. By introducing a parameter-dependent Lyapunov–Krasovskii functional and employing the mode-dependent average dwell time (MDADT) method, results on exponential stability and robust H ∞ performance are proposed. Furthermore, the gains of the output tracking controller with matched system mode are obtained by solving a set of linear matrix inequalities (LIMs), at the same time, the parallel results with the mismatched case are also obtained. Simulation results show that the proposed design scheme not only guarantees tracking performance but also saves communication resources effectively.

Interval Type-2 Fuzzy-Model-Based Sampled-Data Control of an AUV Depth System with Input Saturation

This paper proposes a sampled-data fuzzy controller design technique for an autonomous underwater vehicle (AUV) depth system represented by an interval type-2 (IT-2) fuzzy model, considering input saturation. In the Takagi–Sugeno (T–S) fuzzy model of an AUV depth system, surge velocity is chosen as a premise variable. To address the associated uncertainty with this variable, we employ the IT-2 fuzzy modeling technique. Also, the controller proposed in this paper utilizes time-varying gains, ensuring superior exponential stability compared with traditional fixed gain approaches. Furthermore, a membership function-dependent (MFD) H∞ criterion is employed to enhance robustness for each subsystem individually. Taking into account the mentioned aspects, the controller design condition is derived in the form of linear matrix inequalities (LMIs). Finally, the effectiveness of the proposed method is validated through simulation examples.

Semiglobal exponential stability of the discrete-time Arrow-Hurwicz-Uzawa primal-dual algorithm for constrained optimization

We consider the discrete-time Arrow-Hurwicz-Uzawa primal-dual algorithm, also known as the first-order Lagrangian method, for constrained optimization problems involving a smooth strongly convex cost and smooth convex constraints. We prove that, for every given compact set of initial conditions, there always exists a sufficiently small stepsize guaranteeing exponential stability of the optimal primal-dual solution of the problem with a domain of attraction including the initialization set. Inspired by the analysis of nonlinear oscillators, the stability proof is based on a non-quadratic Lyapunov function including a nonlinear cross term.

Output Feedback for Nonlinear Systems With Nonlinear and Discontinuous Inputs

The paper aims to design a high-gain observer for nonlinear systems with nonlinear and discontinuous sensor signal. The ultimate boundedness and exponential stability of the estimation error of high-gain observer are presented. The performance recovery property of output feedback control using high-gain observer is demonstrated. Simulation examples are illustrated to validate the proposed results of this paper.

Besicovitch Almost Anti-periodic Solution of Octonion-Valued Cohen–Grossberg Neural Networks with Delays on Time Scales

In this work, we put forward a concept of Besicovitch almost anti-periodic functions on time scales, which is new even when time scale T=R\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {T}=\\mathbb {R}$$\\end{document} or Z\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {Z}$$\\end{document}. Based on this, we use the fixed point theorem and analytical techniques to obtain the existence, uniqueness and global exponential stability of Besicovitch almost anti-periodic solutions for a class of octonion-valued Cohen–Grossberg neural networks with time delays on time scales. Finally, the validity of the results is verified by a numerical example.