Exponential Stability Research Articles

Exponential Stability of Impulsive System via Saturated Sliding Mode Control

Exponential Stability of Impulsive System via Saturated Sliding Mode Control

Event-Triggered Sampling Problem for Exponential Stability of Stochastic Nonlinear Delay Systems Driven by Lévy Processes

Event-Triggered Sampling Problem for Exponential Stability of Stochastic Nonlinear Delay Systems Driven by Lévy Processes

Exponential stability for discrete-time singular stochastic systems with semi-Markovian switching

Exponential stability for discrete-time singular stochastic systems with semi-Markovian switching

Exponential stability estimate for derivative nonlinear Schrödinger equation

Exponential stability estimate for derivative nonlinear Schrödinger equation

Quasi-Sure Exponential Stability of Stochastic Differential Delay Systems Driven by G-Brownian Motion

Quasi-Sure Exponential Stability of Stochastic Differential Delay Systems Driven by G-Brownian Motion

Strong stability exponential bound improvement for mode-constrained switching impulsive systems

Strong stability, defined by bounds that decay not only over time but also with the number of impulses, has been established as a requirement to ensure robustness properties for impulsive systems with respect to inputs or disturbances. Most existing results, however, only consider weak stability, where the bounds only decay with time. In this paper, we provide a method for calculating the maximum overshoot and the decay rate for strong global uniform exponential stability for nonlinear switched impulsive systems. We consider mode constrained switching, where not all transitions between subsystems are allowed, and where subsystems may exhibit unstable dynamics in the flow and/or jump maps. Based on direct and reverse mode-dependent average dwell-time and activation-time constraints, we derive stability bounds that can be improved by considering longer switching sequences. We provide an example that shows how to ensure the stability robustness of nonlinear systems with a global state weak linearisation.

Secure Control of Networked Control Systems Under Replay Attacks: A Switching‐Like Approach

ABSTRACTThis paper focuses on the secure control design of networked control systems (NCSs) under replay attacks. Mitigating replay attacks is a challenging task since the statistical similarity between replayed signals and real observations makes them difficult to distinguish. Given the persistence of potential attackers and the probability of individual attack failures, a novel switching‐based replay attack model is introduced. By employing this replay attack model, NCSs vulnerable to replay attacks can be transformed into a class of switching‐like systems. Within the framework of the average dwell time switching strategy and multiple Lyapunov stability theory, sufficient conditions for the mean‐square exponential stability of the underlying system are presented. Compared with the existing control schemes using the delay‐based replay attack model, the proposed secure control method effectively reduces the impact of replay attacks on the control performance. The effectiveness of the proposed approach is validated through simulation experiments carried out on two practical systems.

Practical Exponential Stability of Switched Generalized Homogeneous Positive Nonlinear Systems with Bounded Disturbances

Practical Exponential Stability of Switched Generalized Homogeneous Positive Nonlinear Systems with Bounded Disturbances

Exponential stability for a swelling porous-heat system with thermodiffusion effects and distributed delay term

This work is concerned with the study of the well-posedness and asymptotic behaviour of solutions to a swelling porous system with thermodiffusion effects and distributed delay term. We demonstrate the well-posedness of the solution of the system by using the semigroup approach under suitable assumption on the weight of the distributed delay. Then, we obtain the exponential decay result by using the energy method which is based on the multiplier technique in which we construct an appropriate Lyapunov functional.

Exponential Stability of Higher Order Fractional Neutral Stochastic Differential Equation Via Integral Contractors

ABSTRACTThe well‐posedness results for mild solutions to the fractional neutral stochastic differential system with Rosenblatt process with Hurst index is discussed in this article. To demonstrate the results, the concept of bounded integral contractors is combined with the stochastic result and sequencing technique. In contrast to previous publications, we do not need to specify the induced inverse of the controllability operator to prove the stability results, and the relevant nonlinear function does not have to meet the Lipschitz condition. Furthermore, exponential stability results for neutral stochastic differential systems with Poisson jump have been established. Finally, an application to demonstrate the acquired results is discussed. We demonstrate the fractional Zener model for wave equation obeying the viscoelastic materials as a practical application of the system studied, which is a generalization of classical wave equation.

Pointwise Stabilization in the Laminated Beam Model

We consider two identical beams on top of each other with an adhesive in the middle. A slip occurs naturally in the structure. In this work, we take this slip into account and show that we can stabilize the system exponentially using pointwise controls applied on the axial force and the bending moment. The model consists of three coupled equations. The first two equations are related to the Timoshenko system and the third equation describes the dynamics of the slip. Our result improves previous results in the sense that it addresses the smaller dissipative effect, the point mechanism. To do this, we introduce a new method that allows us to show the exponential stability of systems of partial differential equations with point dissipation.

Tracking control of fully actuated ocean vehicles in a viscous incompressible fluid

This paper addresses the problem of tracking control with a position tracking error constraint of ocean vehicles inside a viscous incompressible fluid, which is described by Navier–Stokes equations (NSEs) perturbed by fluid body force within a bounded domain in three-dimensional space. Since only weak solutions of the NSEs exist globally while global existence of their strong/smooth solutions is a millennium problem, point-wise fluid forces and moments acting on the ocean vehicle are not able to bound. This difficulty is overcome by an appropriate design of control laws and stability analysis of the closed-loop system including the NSEs using a proper extension of the vehicle body. The proposed control design ensures existence of a weak solution and practical exponential stability of the closed-loop system. A simulation on an omni-directional intelligent navigator illustrates the results.

(ω,c)-Asymptotically periodic oscillation of cellular neural networks on time scales with leakage delays and mixed time-varying delays.

In this paper, we introduce the concept of (ω,c)-asymptotic periodicity within the context of translation-invariant time scales. This concept generalizes various types of function, including asymptotically periodic, asymptotically antiperiodic, asymptotically Bloch periodic, and certain unbounded functions on time scales. We investigate some fundamental properties of this class of functions and apply our findings to cellular neural network (CNN) dynamic equations with leakage and mixed time-varying delays. Using time-scale calculus and a method of contradiction, we establish sufficient conditions for the existence of a unique (ω,c)-asymptotically periodic solution for the considered CNNs and their global exponential stability. These results are completely new across all time domains. In addition, we provide numerical examples and simulations to illustrate the effectiveness of our results for various time scales.

New Lyapunov functions for systems with source terms

Abstract Lyapunov functions with exponential weights have been used successfully as a powerful tool for the stability analysis of hyperbolic systems of balance laws. In this paper we extend the class of weight functions to a family of hyperbolic functions and study the advantages in the analysis of 2 × 2 systems of balance laws. We present cases connected with the study of the limit of stabilizability, where the new weights provide Lyapunov functions that show exponential stability for a larger set of problem parameters than classical exponential weights. Moreover, we show that sufficiently large time-delays influence the limit of stabilizability in the sense that the parameter set, for which the system can be stabilized becomes substantially smaller. We also demonstrate that the hyperbolic weights are useful in the analysis of the boundary feedback stability of systems of balance laws that are governed by quasilinear hyperbolic partial differential equations.

Sampled-data controllers and observer-design for uncertain semilinear systems with positivity constraints

This paper deals with the problem of positive stabilization of a class of uncertain semilinear diffusion systems using sampled-data controllers. The conditions for the existence of such controllers are obtained through certain inequalities. By solving these inequalities, we determine upper bounds for the sampling intervals that guarantee exponential stability, as well as the corresponding decay rates. Furthermore, the design of a positive observer for systems with discrete measurements is studied. The stability of the estimation error is ensured through the same LMIs. Numerical simulations are presented to illustrate the effectiveness of the proposed approach.

Exponential Stability of Highly Nonlinear Hybrid Neutral Pantograph Stochastic Systems with Multiple Delays

Exponential Stability of Highly Nonlinear Hybrid Neutral Pantograph Stochastic Systems with Multiple Delays

Exponential Stabilization and Discrete Approximation for Axially Moving Euler–Bernoulli Beam Under Nonlinear Boundary Control

Exponential Stabilization and Discrete Approximation for Axially Moving Euler–Bernoulli Beam Under Nonlinear Boundary Control

Exponential stabilization of memristive neural networks by using integral-type event-trigger scheme

Exponential stabilization of memristive neural networks by using integral-type event-trigger scheme

Stability estimates for a class of neutral type systems with distributed time-varying delay components

This paper investigates new stability estimates for a class of neutral type systems with distributed time-varying delay components. Initially, an appropriate Lyapunov–Krasovskii functional (LKF) is constructed to generate some solution estimates for the considered system. Then, using the estimates obtained in the employed method framework, it is determined whether the solutions are stable or not. The stabilization rates of the solutions at infinity are discussed in the context of asymptotic and exponential stability (ES). Finally, two numerical examples with simulations are presented to demonstrate the applicability of the proposed method on the current results.

Exponential Mean-Square Stabilization Control for Cyber-Physical Systems Under Random DoS Attacks and Transmission Delay

Exponential Mean-Square Stabilization Control for Cyber-Physical Systems Under Random DoS Attacks and Transmission Delay