Finite time stability and controller design for nonlinear impulsive sampled-data systems with applications

2017 ◽  
Vol 70 ◽  
pp. 30-36 ◽  
Author(s):  
Xiaoxiao Lv ◽  
Xiaodi Li
Keyword(s):  
Finite Time ◽  
Controller Design ◽  
Data Systems ◽  
Sampled Data ◽  
Time Stability ◽  
Finite Time Stability

scholarly journals Finite-Time Stability and Controller Design of Continuous-Time Polynomial Fuzzy Systems

2017 ◽  
Vol 2017 ◽  
pp. 1-12
Author(s):  
Xiaoxing Chen ◽  
Manfeng Hu
Keyword(s):  
Continuous Time ◽  
Finite Time ◽  
Fuzzy Systems ◽  
Controller Design ◽  
Semidefinite Program ◽  
Time Stability ◽  
Finite Time Stability ◽  
Polynomial Fuzzy Systems ◽  
Special Cases ◽  
Stability And Stabilization

Finite-time stability and stabilization problem is first investigated for continuous-time polynomial fuzzy systems. The concept of finite-time stability and stabilization is given for polynomial fuzzy systems based on the idea of classical references. A sum-of-squares- (SOS-) based approach is used to obtain the finite-time stability and stabilization conditions, which include some classical results as special cases. The proposed conditions can be solved with the help of powerful Matlab toolbox SOSTOOLS and a semidefinite-program (SDP) solver. Finally, two numerical examples and one practical example are employed to illustrate the validity and effectiveness of the provided conditions.

scholarly journals L∞Control with Finite-Time Stability for Switched Systems under Asynchronous Switching

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Ronghao Wang ◽  
Jianchun Xing ◽  
Ping Wang ◽  
Qiliang Yang ◽  
Zhengrong Xiang
Keyword(s):  
Finite Time ◽  
Switched Systems ◽  
Controller Design ◽  
Average Dwell Time ◽  
Switched System ◽  
Asynchronous Switching ◽  
Time Stability ◽  
Switching Law ◽  
Finite Time Stability ◽  
Exogenous Disturbances

This paper is concerned with the problem of controller design for switched systems under asynchronous switching with exogenous disturbances. The attention is focused on designing the feedback controller that guarantees the finite-time bounded andL∞finite-time stability of the dynamic system. Firstly, when there exists asynchronous switching between the controller and the system, a sufficient condition for the existence of stabilizing switching law for the addressed switched system is derived. It is proved that the switched system is finite-time stabilizable under asynchronous switching satisfying the average dwell-time condition. Furthermore, the problem ofL∞control for switched systems under asynchronous switching is also investigated. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

Admissible Finite-Time Stability and Stabilization of Uncertain Discrete Singular Systems

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
Wenping Xue ◽  
Weijie Mao
Keyword(s):  
Finite Time ◽  
Controller Design ◽  
Singular Systems ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Time Stability ◽  
Finite Time Stability ◽  
Fixed Parameter ◽  
Discrete Singular Systems ◽  
Definition Of

The problems of admissible finite-time stability (AFTS) and admissible finite-time stabilization for a class of uncertain discrete singular systems are addressed in this study. The definition of AFTS is first given. Second, a sufficient condition for the AFTS of the nominal unforced system is established, which is further extended to the uncertain case. Then, a sufficient condition is proposed for the design of a state feedback controller such that the closed-loop system is admissibly finite-time stable for all admissible uncertainties. Both the AFTS and the controller design conditions are presented in terms of linear matrix inequalities (LMIs) with a fixed parameter. Finally, two numerical examples are provided to illustrate the effectiveness of the developed theory.

scholarly journals Finite-Time Vibration-Attenuation Controller Design for Structural Systems with Parameter Uncertainties

2014 ◽  
Vol 6 ◽  
pp. 673174 ◽  
Author(s):  
Yuanchun Ding ◽  
Falu Weng ◽  
Ji Ge ◽  
Liming Liang ◽  
Guoliang Yang
Keyword(s):  
Finite Time ◽  
Closed Loop ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Disturbance Attenuation ◽  
Structural Systems ◽  
Time Stability ◽  
Parameter Uncertainties ◽  
Finite Time Stability ◽  
Vibration Attenuation

The problem of finite-time vibration-attenuation controller design for buildings structural systems with parameter uncertainties is the concern of this paper. The objective of designing controllers is to guarantee the finite-time stability of closed-loop systems with a prescribed level of disturbance attenuation. First, based on matrix transformation, the structural system is described as state-space model, which contains parameter uncertainties. Then, based on finite-time stability analysis method, some sufficient conditions for the existence of finite-time vibration-attenuation controllers are obtained. By solving these conditions, the desired controllers can be obtained for the closed-loop system to be finite-time stable with the performance ∥ z∥2 < γ∥ω∥2. It is shown by the simulation results, that compared with some Lyapunov asymptotic stability results, finite-time stability control can obtain better state responses, especially while the system is under nonzero initial states.

scholarly journals Finite-Time Stability for a Class of Underactuated Systems Subject to Time-Varying Disturbance

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-7 ◽  
Author(s):  
Jie Wu ◽  
Dan Yang ◽  
Xinyi He ◽  
Xiaodi Li
Keyword(s):  
Finite Time ◽  
Design Methodology ◽  
Controller Design ◽  
Underactuated Systems ◽  
Local Form ◽  
Sufficient Condition ◽  
Time Varying ◽  
Time Stability ◽  
Finite Time Stability ◽  
Convergence Performance

Based on the classical finite-time stability theory, the problem of finite-time stability (FTS) for time-varying nonlinear systems is investigated in this paper. Several FTS theorems involving global form and local form are presented, and an estimate of the settling-time of such systems is obtained. As an application, we consider the problem of asymptotic stabilization of the Brockett integrator subject to time-varying disturbance. By the switched finite-time controller design methodology, we establish a sufficient condition to guarantee the relative asymptotic stability. For Brockett-like integrator subject to time-varying disturbance, we achieve better convergence performance. Examples and their simulations are given to demonstrate the applicability of the proposed results.

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