Finite-time Stability Analysis Research Articles

Finite-time stability analysis of homogeneous systems with sector nonlinearities

A class of homogeneous systems with sector nonlinearities is considered in the paper. Sufficient conditions of finite-time (input-to-state) stability are established with the use of new constructive modification of the Implicit Lyapunov Function approach. The proposed conditions are given in the form of linear matrix inequalities. The theoretical results are supported with numerical examples.

Finite-time stability analysis of fractional fuzzy differential equations with time-varying delay involving the generalized Caputo fractional derivative

Finite-time stability analysis of fractional fuzzy differential equations with time-varying delay involving the generalized Caputo fractional derivative

Fractional-Order Degn–Harrison Reaction–Diffusion Model: Finite-Time Dynamics of Stability and Synchronization

This study aims to address the topic of finite-time synchronization within a specific subset of fractional-order Degn–Harrison reaction–diffusion systems. To achieve this goal, we begin with the introduction of a novel lemma specific for finite-time stability analysis. Diverging from existing criteria, this lemma represents a significant extension of prior findings, laying the groundwork for subsequent investigations. Building upon this foundation, we proceed to develop efficient dependent linear controllers designed to orchestrate finite-time synchronization. Leveraging the power of a Lyapunov function, we derive new, robust conditions that ensure the attainment of synchronization within a predefined time frame. This innovative approach not only enhances our understanding of finite-time synchronization, but also offers practical solutions for its realization in complex systems. To validate the efficacy and applicability of our proposed methodology, extensive numerical simulations are conducted. Through this comprehensive analysis, we aim to contribute valuable insights to the field of fractional-order reaction–diffusion systems while paving the way for practical implementations in real-world applications.

Finite time stability analysis for fractional stochastic neutral delay differential equations

Finite time stability analysis for fractional stochastic neutral delay differential equations

Finite time stability analysis of the coupled stochastic reaction–diffusion systems on networks

In this work, we consider a class of coupled stochastic reaction–diffusion systems (CSRDSs, in short) on networks, the criterion on the finite time stability of the trivial solution for CSRDSs on networks is derived by means of the composite Lyapunov function method. To carry out the required results, we establish some useful lemmas firstly for preliminaries. For illustration, an example is given to verify the obtained results.

Imperfect premise matching finite-time filter design for continuous-time Takagi–Sugeno fuzzy systems

An input–output finite-time filtering design problem for a class of delayed Takagi–Sugeno fuzzy systems with external disturbance input is discussed in this paper. Specifically, the filter design uses the imperfect premise matching scheme that relaxes the requirement that the filter and system membership functions be the same. This method can improve the flexibility of the filter design by incorporating membership function information into the input–output finite-time stability analysis. Using the system and filter states, an augmented filtering system is obtained. The required stability criteria are then derived using the Lyapunov–Krasovskii stability theorem and a few recent inequality approaches. Following that, the desired filter gain matrices are determined. The developed filtering design method is validated through some demonstrative examples.

Analysis of finite-time stability in genetic regulatory networks with interval time-varying delays and leakage delay effects

<p>We primarily examined the effect of leakage delays on finite-time stability problems for genetic regulatory networks with interval time-varying delays. Since leakage delays can occur within the negative feedback components of networks and significantly impact their dynamics, they may potentially cause instability or suboptimal performance. The derived criteria encompass both leakage delays and discrete interval time-varying delays through the construction of a Lyapunov-Krasovskii function. We employed the estimation of various integral inequalities and a reciprocally convex technique. Additionally, these models consider lower bounds on delays, which may be either positive or zero, and allow for the derivatives of delays to be either positive or negative. Consequently, new criteria for genetic regulatory networks with interval time-varying delays under the effect of leakage delays are expressed in the form of linear matrix inequalities. Ultimately, a numerical example is presented to show the effect of leakage delays and to emphasize the significance of our theoretical findings.</p>

Finite-Time Stability Analysis and Stabilization of Switched Affine Systems via an Event-Triggered Strategy.

This article investigates the finite-time control problem of the switched affine systems via an event-triggered strategy. It is well known that the existence of affine terms brings great difficulties in analysis of the finite-time property of such systems. Furthermore, the design of the globally feasible event-triggered mechanism (ETM) under a finite-time control framework is challenging. Thus, a two-step hybrid control scheme is proposed in this article. The first step focuses on the event-triggered finite-time control for practical stability, while the second step aims to achieve finite-time stabilization. Particularly, in step one, by constructing the intersection between the affine term's threshold and feasible state region of the established ETM, it is verified that the Zeno behavior can be excluded. Thereafter, an affine state-dependent switching law and sufficient conditions are provided for achieving practical stability. Meanwhile, an estimation for the practical settling time to enter the bounded set is provided. In step two, the criteria for finite-time stabilization of the considered systems are further presented, and an overall settling-time upper bound is derived. Finally, a numerical example is illustrated to demonstrate the effectiveness of our proposed method.

Finite-time stability analysis of singular neutral systems with time delay

<p>This paper studies the finite-time stability problem for a class of singular neutral systems by using the Lyapunov-Krasovskii function approach and regular neutral system theory. The considered systems involve not only the delayed version of the state, but also the delayed version of the derivative of the state. Some sufficient conditions are presented to ensure that the considered systems are regular, impulse-free, and finite-time stable. Three numerical examples are given to illustrate the effectiveness of the proposed methods.</p>

Distributed adaptive control for multiple unmanned aerial vehicles with state constraints and input quantization

AbstractThis paper investigates the distributed fault‐tolerant tracking control (FTTC) problem for multiple unmanned aerial vehicles (UAVs) in the presence of state constraints, input quantization and actuator failures. The unified barrier function (UBF) is first developed to convert the original constrained system model into an unconstrained one, which accomplishes the dynamic constraints of all states. Moreover, a cerebellar model neural network (CMNN) is introduced to estimate the lumped effect of unknown disturbances and actuator failures. Then, a distributed formation flight fault‐tolerant controller (FTC) is designed to guide the UAVs along the desired trajectories based on sliding mode manifold and dynamic surface control technique. Meanwhile, the unknown input chattering and hysteresis quantizer errors in the UAVs system are simultaneously handled by adding the compensation term of FTC. Furthermore, the finite time stability analysis is implemented for all tracking errors and synchronization errors of the cooperative flight control system (CFCS). Finally, a comparative simulation is conducted to demonstrate the effectiveness of the FTTC scheme proposed in this study.

Finite time SF bifurcation and stability analysis for stochastic time-varying delay system

In this paper, it is found that the systems alternate between oscillatory and steady states in studying the stability of a class of stochastic dynamical systems with fast time-varying periodic delays. We propose a new definition of bifurcation, State Flip (SF) bifurcation, by using the abrupt change in the dwell time ratio of two states. Taking the amplitude of the time-varying delay function δ as the bifurcation parameter, we investigate the dynamics of the evolution of a time-varying delay system driven by Gaussian white noise. Firstly, we convert systems with fast time-varying periodic delays into comparative systems with distributed delays, which in turn are converted into stochastic systems with constant delays for discussion. In order to reduce the stochastic delay equation to the average Itô equation, we adopted the stochastic averaging method and the generalized central manifold theory. It is used to capture the one-dimensional slow variables of a system near the critical state of the transition between two steady states during the evolution of the system. We then find that as the amplitude increases from weak to strong, the stochastic time-varying delay system changes from a two-period oscillation to alternating between oscillation and steady, and finally to a steady state. Lastly, we perform numerical simulations of the original stochastic time-varying delay system and the transformed two-dimensional stochastic constant time-delay system respectively to verify that the ideas and methods in this paper are reasonable and effective.

Finite-time stability analysis and control of stochastic SIR epidemic model: A study of COVID-19

Finite-time stability analysis is a powerful tool for understanding the long-term behavior of epidemiological models and has been widely used to study the spread of infectious diseases such as COVID-19. In this paper, we present a finite-time stability analysis of a stochastic susceptible–infected–recovered (SIR) epidemic compartmental model with switching signals. The model includes a linear parameter variation (LPV) and switching system that represents the impact of external factors, such as changes in public health policies or seasonal variations, on the transmission rate of the disease. We use the Lyapunov stability theory to examine the long-term behavior of the model and determine conditions under which the disease is likely to die out or persist in the population. By taking advantage of the average dwell time method and Lyapunov functional (LF) method, and using novel inequality techniques the finite-time stability (FTS) criterion in linear matrix inequalities (LMIs) is developed. The finite-time stability of the resultant closed-loop system, with interval and linear parameter variation (LPV), is then guaranteed by state feedback controllers. By analyzing the modified SIR model with these interventions, we are able to examine the efficiency of different control measures and determine the most appropriate response to the COVID-19 pandemic and demonstrate the efficacy of the suggested strategy through simulation results.

Backstepping-Based Finite-Time Control for High-Order Discrete-Time Systems

This paper studies the finite-time control of high-order discrete-time nonlinear systems. A novel backstepping based nonsmooth finite-time controller design method is established through recursive computation. Under proposed control scheme, the finite-time stability analysis is given from the last subsystem to the first subsystem, and the settling time can be estimated. An example is given to verify the method.

Filippov's Solution and Finite-Time Stability of Stochastic Systems for Discontinuous Control

In this paper, a suite of theoretic tools is provided for discontinuous control design and finite-time stability analysis of a class of stochastic differential systems. The notion of Filippov&#x0027;s solutions for stochastic differential systems is proposed, and the corresponding solution existence problem is explored. The classical It&#x00F4; differentiation formula is generalized for quasi-<inline-formula><tex-math notation="LaTeX">$C_{0}^{2}(\mathbb {R}^{n},\mathbb {R})$</tex-math></inline-formula>-class functions along Filippov&#x0027;s solutions of stochastic differential systems, and two involved set-valued stochastic integrals are introduced with a study on their properties. Some finite-time stability results of stochastic differential systems are revealed with Filippov&#x0027;s solutions, and one of them is applied to neural synchronization, together with case simulations.

Finite time course keeping control for unmanned surface vehicles with command filter and rudder saturation

This paper studies the problem of course keeping control for unmanned surface vehicle (USV) with servo dynamic characteristics, environmental disturbances and model’s uncertainties, and rudder saturation. Considering the characteristics of the rudder servo system (RSS), a nonlinear Norrbin model with second-order rudder is reconstructed, and proposes a finite time simple and practical course controller by the finite time dynamic surface control (FTDSC) technology, which achieve excellent finite time command filter. Then, the nonlinear disturbance observer (NDOB) is applied to estimate the lumped disturbances, which is easy to implement in engineering. Meanwhile, the bandwidth between the controller and the observer is studied, which affects the convergence speed of the observer. Besides, finite time dynamic auxiliary systems with smooth switching function (FTADS-SSF) is designed to compensate for rudder physical constraints with finite time convergence. Further practical finite time stability analysis indicates that the entire system is uniformly ultimately bounded (UUB). Finally, simulation comparison results have been demonstrated the proposed strategy.

A Linear Time-Varying Inequality Approach for Prescribed Time Stability and Stabilization.

This article studies the problem of finite-time, fixed-time, and prescribed-time stability analysis and stabilization. First, a linear time-varying (LTV) inequality-based approach is introduced for prescribed-time stability analysis. Then, it is shown that the existing nonlinear Lyapunov inequalities-based finite- and fixed-time stability criteria can be recast into the unified framework of the LTV inequality-based approach for prescribed-time stability. Finally, the unified LTV inequality-based approach is used to solve the global prescribed-time stabilization problem of the attitude control system of a rigid spacecraft with disturbance, and a bounded nonlinear time-varying controller is proposed via back stepping. Numerical simulations are presented to show the effectiveness of the proposed methods.

Finite-time stability analysis for switched homogeneous positive systems: A variable cyclic dwell-time approach

In this paper, the finite-time stability for a class of switched homogeneous positive systems (SHPSs) is discussed. First, each subsystem is assumed to be finite-time stable and the degree of homogeneity satisfies [Formula: see text]. A new variable cyclic dwell-time approach is proposed, which allows for greater flexibility in switching signal design than the existing cyclic dwell-time approach. By virtue of the variable cyclic dwell-time and switched max-type separated Lyapunov function methods, the finite-time stability criterion for SHPSs is established and the settling time is obtained. Moreover, the stability result is extended to SHPSs containing unstable subsystems. Finally, two simulation examples are provided to demonstrate the effectiveness of the theoretical analysis.

Finite-time stability analysis of switched systems with actuator saturation based on event-triggered mechanism

Under the event-triggered scheme, this note focuses on the problem of finite-time stability analysis of the switched system with controller failure and external interference. Firstly, in order to save network communication resources, the mixed event-triggered condition is considered. This mechanism can not only avoid Zeno phenomenon, but also use the sampled information more effectively. In addition, the saturation characteristics of the actuator are fully considered, which can further reduce the number of triggers. According to different event-triggered conditions, an algorithm is proposed to estimate the attraction domain. Then, through the Lyapunov-Krasovskii functional approach and average dwell time technology, the closed-loop switched system is analyzed. The determination condition of finite-time stability is obtained. To illustrate the advantages of our established results, a numerical example is finally given. In addition to saving communication resources, the system stability is guaranteed. The advantages of the proposed method can be verified by simulation.

Finite-time stability of dynamical system under event-triggered hybrid control

Finite-time stability analysis for general dynamical system is presented under event-triggered control mechanism in this paper. By designing a novel event-triggered mechanism and a hybrid controller involving impulsive control and sampling control, the sufficient finite-time stability criteria are derived and the Zeno behavior is excluded simultaneously. Typical numerical examples involving the finite-time stabilization and synchronization of chaotic systems are given to show the effectiveness of our theoretical criteria.

Finite-time and fixed-time stability analysis for time-varying systems: A dual approach

In this paper we present a new dual approach to investigating the stability of the system of two nonautonomous ODE with the right-hand side being only Lebesgue measurable with respect to time t. We define a new dual Lapunov function S which depends on three variables, and we give sufficient conditions for finite and fixed-time stability for the system using a dual Hamilton-Jacobi inequality and taking advantage of a class of functions M and MB. This method allows simultaneous investigation of the finite and fixed-time stability of the primary and the dual equation. We give some examples to illustrate the results obtained. As an application of this dual approach, we define the region of attraction and illustrate with an example.