scholarly journals A Generalization of the Cauchy-Schwarz Inequality and Its Application to Stability Analysis of Nonlinear Impulsive Control Systems

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-7 ◽  
Author(s):  
Yang Peng ◽  
Jiang Wu ◽  
Limin Zou ◽  
Yuming Feng ◽  
Zhengwen Tu
Keyword(s):  
Stability Analysis ◽  
Control Systems ◽  
Impulsive Control ◽  
Schwarz Inequality ◽  
Sufficient Condition ◽  
Numerical Example ◽  
Impulsive Control Systems ◽  
The Stability

In this paper, we first present a generalization of the Cauchy-Schwarz inequality. As an application of our result, we obtain a new sufficient condition for the stability of a class of nonlinear impulsive control systems. We end up this note with a numerical example which shows the effectiveness of our method.

scholarly journals Stability Analysis for Nonlinear Impulsive Control System with Uncertainty Factors

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Zemin Ren ◽  
Shiping Wen ◽  
Qingyu Li ◽  
Yuming Feng ◽  
Ning Tang
Keyword(s):  
Control System ◽  
Stability Analysis ◽  
Parameter Uncertainty ◽  
Impulsive Control ◽  
Schwarz Inequality ◽  
Sufficient Condition ◽  
Uncertainty Factors ◽  
Numerical Example ◽  
Gain Error ◽  
The Stability

Considering the limitation of machine and technology, we study the stability for nonlinear impulsive control system with some uncertainty factors, such as the bounded gain error and the parameter uncertainty. A new sufficient condition for this system is established based on the generalized Cauchy–Schwarz inequality in this paper. Compared with some existing results, the proposed method is more practically applicable. The effectiveness of the proposed method is shown by a numerical example.

scholarly journals Stability analysis of impulsive control systems

2003 ◽  
Vol 37 (12-13) ◽  
pp. 1357-1370 ◽  
Author(s):  
Xinzhi Liu ◽  
Yanqun Liu ◽  
Kok Lay Teo
Keyword(s):  
Stability Analysis ◽  
Control Systems ◽  
Impulsive Control ◽  
Impulsive Control Systems

On the stability of networked impulsive control systems

2011 ◽  
Vol 22 (17) ◽  
pp. 1952-1968 ◽  
Author(s):  
Zhi-Hong Guan ◽  
Jian Huang ◽  
Guanrong Chen ◽  
Ming Jian
Keyword(s):  
Control Systems ◽  
Impulsive Control ◽  
Impulsive Control Systems ◽  
The Stability

scholarly journals Iterative stability analysis for general polynomial control systems

2021 ◽  
Author(s):  
Bo Xiao ◽  
Hak-Keung Lam ◽  
Zhixiong Zhong
Keyword(s):  
Stability Analysis ◽  
Lyapunov Function ◽  
Control Systems ◽  
Polynomial System ◽  
Stability Conditions ◽  
General Polynomial ◽  
Main Challenge ◽  
Detailed Simulation ◽  
Feasible Solutions ◽  
The Stability

AbstractThe main challenge of the stability analysis for general polynomial control systems is that non-convex terms exist in the stability conditions, which hinders solving the stability conditions numerically. Most approaches in the literature impose constraints on the Lyapunov function candidates or the non-convex related terms to circumvent this problem. Motivated by this difficulty, in this paper, we confront the non-convex problem directly and present an iterative stability analysis to address the long-standing problem in general polynomial control systems. Different from the existing methods, no constraints are imposed on the polynomial Lyapunov function candidates. Therefore, the limitations on the Lyapunov function candidate and non-convex terms are eliminated from the proposed analysis, which makes the proposed method more general than the state-of-the-art. In the proposed approach, the stability for the general polynomial model is analyzed and the original non-convex stability conditions are developed. To solve the non-convex stability conditions through the sum-of-squares programming, the iterative stability analysis is presented. The feasible solutions are verified by the original non-convex stability conditions to guarantee the asymptotic stability of the general polynomial system. The detailed simulation example is provided to verify the effectiveness of the proposed approach. The simulation results show that the proposed approach is more capable to find feasible solutions for the general polynomial control systems when compared with the existing ones.

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