Finite-time Stability Of Nonlinear Systems Research Articles

Finite-Time Stabilization of Nonlinear Systems via Hybrid Control and Application to State Estimation of Complex Networks

Finite-Time Stabilization of Nonlinear Systems via Hybrid Control and Application to State Estimation of Complex Networks

Finite-Time Stability of Nonlinear Systems With Delayed Impulses

Finite-Time Stability of Nonlinear Systems With Delayed Impulses

Practical Finite-Time Stability of Nonlinear Systems With Delayed Impulsive Control

Practical Finite-Time Stability of Nonlinear Systems With Delayed Impulsive Control

Assessing the finite-time stability of nonlinear systems by means of physics-informed neural networks

Assessing the finite-time stability of nonlinear systems by means of physics-informed neural networks

Effect of saturation structure on finite-time stabilization of nonlinear systems with impulsive disturbance

This paper studies the finite-time stabilization (FTS) of nonlinear systems with impulsive disturbance, where the effect of saturation structure on the control input is fully considered. By establishing a potential relationship between saturation structure and impulsive disturbance, some FTS criteria are presented via a class of saturated control input, where estimations of domain of attraction and settling-time are derived. Compared with the control input without saturation structure, the constraints on impulse time sequence are strengthened to guarantee that the saturated control input has an effective stabilizing effect on the system. Based on such constraints, the system subjected to impulsive disturbance can still achieve FTS. Then theoretical results are applied to finite-time synchronization for a class of impulsive dynamical networks. Finally, two examples and their simulations are given to illustrate the effectiveness of the proposed results.

Robust finite-time stability of nonlinear systems involving hybrid impulses with application to sliding-mode control.

This paper is concerned with the robust finite-time stability and stabilization of impulsive systems subject to hybrid disturbances that consists of external disturbances and hybrid impulses with time-varying jump maps. First, the global finite-time stability and local finite-time stability of a scalar impulsive system are ensured by the analysis of cumulative effect of hybrid impulses. Then, asymptotic stabilization and finite-time stabilization of second-order system subject to hybrid disturbances are achieved by linear sliding-mode control and non-singular terminal sliding-mode control. It shows that the stable systems under control are robust to external disturbances and hybrid impulses with non-destabilizing cumulative effect. If the hybrid impulses have destabilizing cumulative effect, the systems are also capable of absorbing the hybrid impulsive disturbances by the designed sliding-mode control strategies. Finally, the effectiveness of theoretical results is verified by numerical simulation and the tracking control of linear motor.

Finite-time stabilization of nonlinear systems via impulsive control with state-dependent delay

This paper focuses on the issue of finite-time stability for a general form of nonlinear systems subject to state-dependent delayed impulsive controller. Based on the Lyapunov theory and the impulsive control theory, sufficient conditions for finite-time stability (FTS) and finite-time contractive stability (FTCS) are obtained. Additionally, we apply theoretical results to finite-time synchronization of chaotic systems and design the effective state-dependent delayed impulsive controllers in terms of techniques of linear matrix inequality (LMI). Finally, we present two numerical examples of finite-time synchronization of cellular neural networks and Chua’s circuit to verify the effectiveness of our results.

A New Design to Finite-Time Stabilization of Nonlinear Systems With Applications to General Neural Networks

The finite-time stabilization problem of nonlinear systems is investigated in this paper. Firstly, to improve the precision of settling time of nonlinear system, a new finite-time stability theorem is established, and a higher precision settling time is derived from it. Moreover, by theoretical derivation, we prove that the corresponding settling time is more accurate than the existing results. Secondly, as an application, a new class of finite-time protocol framework, which unifies continuous protocol and discontinuous ones into a uniform formula, is designed to solve the finite-time stabilization problem of the general neural network system, and it can bring to a continuous control protocol and a discontinuous control protocol through choosing different design parameters. It is shown that the convergence rate is improved and also the corresponding settling time is upper bounded by some positive constant independent of initial conditions, which makes it convenient and flexible to adjust the settling time by adjusting design parameters. Finally, two numerical examples are provided to illustrate the effectiveness of our theoretical results.

Finite-time stability of nonlinear systems with state-dependent delayed impulses

This paper addresses the issue of finite-time stability (FTS) and finite-time contractive stability (FTCS) of nonlinear systems involving state-dependent delayed impulsive perturbation. Several sufficient conditions are obtained by using theories of impulsive control and Lyapunov stability. The relation between impulsive perturbation and state-dependent delay is established to achieve FTS and FTCS. For time-varying nonlinear system and nonlinear system with fixed parameters, we derive some sufficient conditions based on the main thought of this paper, respectively. Finally, three numerical examples are provided to illustrate the effectiveness and validity of achieved results.

Finite-time stabilization of nonlinear systems using an event-triggered controller with exponential gains

This paper investigates the finite-time stabilization for a class of nonlinear systems by proposing a new event-triggered controller. The novelty lies in that, by introducing an exponential term, the control gains are exponential alterable in the interval of two adjacent event instants. Moreover, based on the proposed controller, a specific event-triggered scheme with a new type of error function is also derived to stabilize the concerned system in a finite time. In addition, a positive lower bound of the inter-execution is obtained, such that the Zeno behaviors can be avoided. Finally, illustrative examples are provided to verify that the overall amount of triggered events can be reduced by utilizing the proposed method in this paper.

Finite‐time stability of non‐linear systems with impulsive effects due to logic choice

This study is concerned with the finite-time stability of non-linear systems with impulsive effects due to logic choice. Firstly, we introduce a class of non-linear systems with logic-induced impulses and it generalises the model established in Suo and Sun (2015). Then, based on semi-tensor product technique, several criteria for finite-time stability for the system are given. Finally, two numerical examples are provided to illustrate authors' results.

A new switching design to finite-time stabilization of nonlinear systems with applications to neural networks

This paper is concerned with the optimal finite-time stabilization problem for nonlinear systems. For the given stabilization strength, a new switching protocol is designed to stabilize the system with a fast speed. The obtained protocol covers both continuous control and discontinuous one under the framework of Filippov solutions. Some criteria are discussed in detail on how to choose an optimal protocol such that the finite stabilization time can be shortened. Finally, the main theory results are applied to the general neural networks by one numerical example to illustrate the effectiveness of the proposed design method.

Global Asymptotic and Finite-time Stability for Nonlinear Systems

摘要: 针对一类全矩阵形式的非线性系统, 研究其全局稳定性及有限时间镇定问题. 首先, 全矩阵形式非线性系统被分成上三角形式和下三角形式非线性系统的加和, 并针对下三角形式非线性系统, 利用加幂积分方法, 自上而下地设计系统的全局稳定控制器; 其次, 在上面控制器作用下, 证明全矩阵形式系统在一个给定领域内是局部渐近稳定的; 最后, 运用自下而上的顺序, 一种嵌套饱和方法被用到上述控制器中, 通过调节饱和度, 使得闭环系统全局渐近稳定. 此外, 在适当的条件下, 可以得到全矩阵形式非线性系统的全局有限时间稳定性. 关键词: 全局稳定 / 非线性系统 / 加密积分方法 / 有限时间镇定

Finite-Time Stabilization of Nonlinear Systems With Parametric and Dynamic Uncertainties

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> In this note, non-smooth finite-time stabilization of nonlinear systems with parametric and dynamic uncertainties is investigated. To solve this problem, the input-to-state stability property is used to characterize unmeasured dynamic uncertainties. A constructive partial-state control design is proposed on the basis of involved combined use of Lyapunov, backstepping and input-to-state stability techniques. Under small-gain type local conditions, a solution for the finite-time regulation of a class of uncertain nonlinear systems is obtained. </para>

Global finite-time stabilization of a class of uncertain nonlinear systems

This paper studies the problem of finite-time stabilization for nonlinear systems. We prove that global finite-time stabilizability of uncertain nonlinear systems that are dominated by a lower-triangular system can be achieved by Hölder continuous state feedback. The proof is based on the finite-time Lyapunov stability theorem and the nonsmooth feedback design method developed recently for the control of inherently nonlinear systems that cannot be dealt with by any smooth feedback. A recursive design algorithm is developed for the construction of a Hölder continuous, global finite-time stabilizer as well as a C 1 positive definite and proper Lyapunov function that guarantees finite-time stability.