Exponential Stability Analysis Research Articles

An Improved Method for Exponential Stability Analysis of Switched Delay Systems Under Constrained Switching

An Improved Method for Exponential Stability Analysis of Switched Delay Systems Under Constrained Switching

Exponential stability analysis in mean square for a class of stochastic delay differential equations

Exponential stability analysis in mean square for a class of stochastic delay differential equations

Robustness analysis of exponential stability of fuzzy inertial neural networks through the estimation of upper limits of perturbations

This paper characterizes the robustness of exponential stability of fuzzy inertial neural network which contains time delays or stochastic disturbance through the estimation of upper limits of perturbations. By utilizing Gronwall-Bellman lemma, stochastic analysis, Cauchy inequality, the mean value theorem of integrals, as well as the properties of integrations, the limits of both time delays and stochastic disturbances are derived in this paper which can make the disturbed system keep exponential stability. The constraints between the two types of disturbances are provided in this paper. Examples are offered to validate our results.

Analysis and verification of uniform moment exponential stability for stochastic hybrid systems with Poisson jump

Analysis and verification of uniform moment exponential stability for stochastic hybrid systems with Poisson jump

Robust predictive fault-tolerant switching control for discrete linear systems with actuator random failures

Under the condition that state variables are unavailable, a robust predictive fault-tolerant switching control method is proposed for discrete linear systems with actuator random failures. The randomness of failures is described in terms of conditional probabilities. Then, a transfer probability matrix is established to predict the probability of state change. A model incorporating the system state deviation and tracking error is further developed to enhance the regulation of the controller. By using related theories, sufficient conditions for the stability of the system are obtained. Furthermore, average dwell times for the system are obtained according to exponential stability analysis. These times and the matrix form conditions for the output feedback fault-tolerant switching controller to switch between conventional control and fault-tolerant control. Based on the previous work, the research on disturbances and set-point changes has been extended. The feasibility of the method is verified by a case study of the pressure-holding phase.

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.

Stability of conformable fractional time-varying linear systems

In this paper, we investigate the exponential and asymptotic stability analysis of conformable fractional linear time-varying systems. We propose sufficient conditions for testing the asymptotic and exponential stability of conformable differential systems by using the notion of stable functions and differential Lyapunov inequalities. Furthermore, we apply the developed approach to the problem of conformable stabilisation and observer design for conformable fractional linear time-varying systems.

The split step theta balanced numerical approximations of stochastic time varying Hopfield neural networks with distributed delays

In this paper, split step theta balanced Euler approximations for stochastic time-varying delay Hopfield neural networks (HNN) with distributed delays are examined for their exponential stability and strong convergence. The primary goal of this study is to determine how the stochastic HNN time varying delay term affects the analysis of numerically almost sure exponential stability. It became apparent that numerical solutions for stochastic Hopfield neural networks with time-varying and distributed delay functions had not been thoroughly explored. Hence, our research focused on probing into the realms of strong convergence and almost sure exponential stability through the lens of split-step theta-balanced Euler approximations. We examine the stability qualities using the discrete semimartingale convergence theorem. Additionally, we developed the theoretical findings pertaining to the split-step theta balanced Euler approximations almost sure exponential stability analysis and the analysis of the strong convergence order 1/2 in the mean of the global error. The theoretical results are validated through numerical experimentation.

Homogeneity-based exponential stability analysis for conformable fractional-order systems

UDC 517.9 We study the exponential stability of homogeneous fractional time-varying systems, and the existence of Lyapunov homogeneous function for the conformable fractional homogeneous systems. We also prove that local and global behaviors are similar. A numerical example is given to illustrate the efficiency of the obtained results.

Exponential stability and numerical analysis of Timoshenko system with dual‐phase‐lag thermoelasticity

AbstractThis study aims to investigate the well‐posedness and stability of a thermoelastic Timoshenko system with non‐Fourier heat conduction. Specifically, we analyze the system using the dual‐phase‐lag (DPL) model, which incorporates two thermal relaxation times, and , to model non‐instantaneous heat propagation. Applying the semigroup approach, we demonstrate the existence and uniqueness of the solutions. Subsequently, we introduce a novel stability parameter using the multiplier method. Exponential decay is proven for the case of with . Using Gearhart–Prüss theorem, we show the lack of exponential stability when and . Numerically, we present a fully discrete approximation using the finite element method and the backward Euler scheme, and we provide some numerical simulations to show the discrete energy decay and the behavior of solutions.

LMIs-based exponential stabilization for interval delay systems via congruence transformation: Application in chaotic Lorenz system

This paper investigates the stochastic Takagi-Sugeno (T-S) fuzzy uncertainty-dependent state feedback sampled-data control, asymptotical stability and exponential stability analysis for a class of stochastic T-S fuzzy system with measurable uncertainties, mixed interval time varying delays and Gaussian white noise. Firstly, the T-S fuzzy model and stochastic Bernoulli theory are employed to approximate the system plant. Secondly, the stochastic T-S fuzzy uncertainty-dependent state feedback sampled-data controller is designed via uncertainty-dependent parameters and the hold times series of sampled-data. Thirdly, the Bernoulli probability distribution is employed to describe the random occurrence characteristic of multipath packet dropouts. Three classes of delay-dependent stability conditions in terms of linear matrix inequalities (LMIs) are derived for the closed-loop system. The multiple integral fuzzy-basis-dependent Lyapunov functional and augmented state variable are employed to derive the delay-dependent stability conditions, then the closed-loop system is asymptotically stable and exponentially stable. The congruence transformation method and prescribed H-infinity performance functional are employed to derive the less conservative delay-dependent stability conditions, and the prescribed H-infinity performance is guaranteed. The relaxation matrix and congruence transformation method are employed to design the linear transformation equalities and congruence transformation matrices, then the controller gain matrix is determined and computation complexity of solving LMIs is reduced. Finally, the proposed method is applied in the chaotic Lorenz system to show the effectiveness and advantage of proposed method.

Absolute exponential stability of switching Lurie systems with time-varying delay via dwell time switching

This paper addresses the absolute exponential stability analysis for switching Lurie systems with time-varying delay. With the switching time-varying Lyapunov functions technique, sufficient conditions in terms of linear-matrix inequalities are presented to ensure the absolute exponential stability of switching Lurie systems with time-varying delay under mode-dependent dwell time switching signals. Furthermore, the conservatism of the proposed method for stability analysis is studied. Simulation examples illustrate the validity of the obtained results.

Enhanced Exponential Stability Analysis for Switched Linear Time-Varying Delay Systems Under Admissible Edge-Dependent Average Dwell-Time Strategy

This article focuses on the exponential stability analysis for the switched linear systems with time-varying delay. By constructing a new augmented multiple Lyapunov–Krasovskii functional, containing time-varying delay information, coupling of current and delayed states, state integral, and state derivative terms the feasibility of the stability condition is considerably enhanced. Besides, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$</tex-math> </inline-formula> -order canonical Bessel–Legendre integral inequality and the convex function property are utilized to give more relaxed criteria. On the other hand, for the first time, more flexible switching is employed with an admissible edge-dependent average dwell-time strategy for the switched time-varying delay systems (STDSs). Novel improved delay-dependent stability conditions are expressed by two theorems in the form of linear matrix inequalities which can be used to guarantee the exponential stability of the STDSs in the different delay conditions. Finally, significant improvements over the state-of-the-art in terms of delay upper bound, exponential decay rate, and dwell time are presented by simulating two numerical examples and one practical example including streams water quality preserving.

Robust exponential stability analysis of switched systems under switching boundary mismatch

AbstractSwitching boundary is an integral part of the switched system, but the existing literature on switched systems does not focus on the system under switching boundary mismatch. In this article, the switching boundary mismatch is considered, and the control strategy based on observation algorithm is designed for the state dependent switched system. By implementing the proposed strategy, the system can realize robust exponential stability and track the desired trajectory. Since the switching boundary mismatch is unmeasurable, an observation algorithm is designed. Combining the observation algorithm and iterative learning control law, the new control strategy can be derived. According to the Lyapunov stability theory and mode dependent average dwell time method, the robust exponential stability conditions of the closed‐loop system based on linear matrix inequalities are given. The mode dependent average dwell time of each subsystem can be solved simultaneously. Finally, simulations have been taken to verify the designed strategy can render the closed‐loop system achieve robust exponential stability and can track the desired trajectory.

Global exponential stability analysis for tick population model with delayed sub-linear Gamma-Ricker nonlinearities

We argue that self-regulation in tick population dynamics in the natural world is not associated with the egg-production saturation, that was normally assumed in existing literature and modeled using the Ricker reproduction function. We argue that the nonlinearity and self-regulatory inhibition appear in the synergistic effect of tick cooperation and the crowding within groups, and an appropriate nonlinearity can be the sub-linear Gamma-Ricker function. We also noticed that the diapaused development leads to multiple time lags in a structured tick population dynamics model, leading to a scalar delay differential equation with two time lags appearing in the sub-linear Gamma-Ricker nonlinearity. This model has always one and only one positive equilibrium. Here we develop sharp conditions for this model to exhibit persistence and global convergence behaviors.

Global Exponential Stability Analysis of Commutative Quaternion-Valued Neural Networks with Time Delays on Time Scales

Global Exponential Stability Analysis of Commutative Quaternion-Valued Neural Networks with Time Delays on Time Scales

Exponential stability analysis for nonlinear time-varying perturbed systems on time scales

&lt;abstract&gt;&lt;p&gt;This paper is concerned with the stability of nonlinear time-varying perturbed system on time scales under the assumption that the corresponding linear time-varying nominal system is uniformly exponentially stable. Some less conservative sufficient conditions for uniform exponential stability and uniform practical exponential stability are proposed by imposing different assumptions on the perturbation term. Compared with the traditional exponential stability results of perturbed systems, the time derivatives of related Lyapunov functions in this paper are not required to be negative definite for all time. The main tools employed are two Gronwall's inequalities on time scales. Some examples are also given to illustrate the effectiveness of the theoretical results.&lt;/p&gt;&lt;/abstract&gt;

Model Predictive Control for Linear Uncertain Systems Using Integral Quadratic Constraints

In this work, we propose a tube-based MPC scheme for state- and input-constrained linear systems subject to dynamic uncertainties characterized by dynamic integral quadratic constraints (IQCs). In particular, we extend the framework of $\rho$-hard IQCs for exponential stability analysis to external inputs. This result yields that the error between the true uncertain system and the nominal prediction model is bounded by an exponentially stable scalar system. In the proposed tube-based MPC scheme, the state of this error bounding system is predicted along with the nominal model and used as a scaling parameter for the tube size. We prove that this method achieves robust constraint satisfaction and input-to-state stability despite dynamic uncertainties and additive bounded disturbances. A numerical example demonstrates the reduced conservatism of this IQC approach compared to state-of-the-art robust MPC approaches for dynamic uncertainties.

Constructive finite-dimensional boundary control of stochastic 1D parabolic PDEs

Recently, a constructive method for the finite-dimensional observer-based control of deterministic parabolic PDEs was suggested by employing a modal decomposition approach. In this paper, for the first time we extend this method to the stochastic 1D heat equation with nonlinear multiplicative noise. We consider the Neumann actuation and study the observer-based as well as the state-feedback controls via the modal decomposition approach. We employ either trigonometric or polynomial dynamic extension. For observer-based control we consider a noisy boundary measurement. First, we show the well-posedness of strong solutions to the closed-loop systems. Then by suggesting a direct Lyapunov method and employing Itô’s formula, we provide mean-square L2 exponential stability analysis of the full-order closed-loop system, leading to linear matrix inequality (LMI) conditions for finding the observer dimension and as large as possible noise intensity bound for the mean-square stabilizability. We prove that the LMIs are always feasible for small enough noise intensity and large enough observer dimension (for observer-based control). We further show that in the case of state-feedback and linear noise, the system is always stabilizable for noise intensities that guarantee the stabilizability of the stochastic finite-dimensional part of the closed-loop system with deterministic measurement. Numerical simulations are carried out to illustrate the efficiency of our method. For both state-feedback and observer-based controls, the trigonometric extension always allows for a larger noise than the polynomial one in the example.

Exponential stability and stabilization of positive T‐S fuzzy delayed systems

AbstractThe analysis of positive nonlinear delayed systems is of great importance for many real‐world applications. Such systems' stability and stabilization assessment is still an open topic, and there is limited literature on this field. Moreover, further convergence conditions should be considered for many experimental processes, such as exponential stability analysis, which is highly important. Considering the above, we deal in this study with the problem of exponential stability and stabilization of nonlinear fuzzy positive systems with delay. We establish exponential stability criteria using Lyapunov–Krasovskii functional (LKF) and a delay bi‐decomposition approach for bounded and time‐varying delayed systems. The obtained results are then extended to the exponential stabilization case. The control law is designed using Parallel distributed compensation (PDC). The proposed approach, formulated in terms of linear matrix inequalities (LMIs), allows reducing the conservativeness of the delay‐dependent conditions. A comparative study is presented to illustrate the superiority of our method. Moreover, simulation results for the two tanks process show the advantages of the proposed control design.