Kinetic Lyapunov Function for Stability Analysis of Nonlinear Control Systems

1961 ◽  
Vol 83 (1) ◽  
pp. 91-94 ◽  
Author(s):  
S. S. L. Chang
Keyword(s):  
Stability Analysis ◽  
Nonlinear System ◽  
Asymptotic Stability ◽  
Lyapunov Function ◽  
Control Systems ◽  
Local Stability ◽  
Nonlinear Control Systems ◽  
Sufficient Condition ◽  
State Variables ◽  
Derivatives Of

A kinetic Lyapunov function is a Lyapunov function of the first derivatives of the state variables. Its use leads to a sufficient condition for the asymptotic stability in the large of a general nonlinear system without hysteresis. The foregoing sufficient condition is similar to but more stringent than the local stability condition for linearized systems.

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.

Stabilization of Nonlinear Systems Using Linear Observers

1974 ◽  
Vol 96 (1) ◽  
pp. 55-60 ◽  
Author(s):  
R. E. Strane ◽  
W. G. Vogt
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Asymptotic Stability ◽  
Nonlinear Equations ◽  
Linear Approximation ◽  
Asymptotically Stable ◽  
State Variables ◽  
Finite Region ◽  
Linear Portion ◽  
Linear Observer

In this paper, it is shown that a linear observer can always be designed to stabilize a nonlinear system which contains a Lur’e type nonlinearity in the sector [0, k], where k is finite, if both the output of the nonlinearity and a completely observable output of the linear portion are available as inputs to the observer. In case a completely observable output is not available from the linear portion, stabilization is shown to be possible if the original linear approximation of the system is asymptotically stable or those state variables corresponding to the unstable eigenvalues are available. It is also established that a linear observer can be used to guarantee that a finite region of asymptotic stability exists for a plant described by a more general set of nonlinear equations, and in some cases the domain of asymptotic stability can be made as large as desired.

scholarly journals Stability Analysis of a Nonlinear System with Different Growth Functions

2018 ◽  
Vol 37 ◽  
pp. 111-119
Author(s):  
Md Kamrujjaman ◽  
Ashrafi Meher Niger
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Nonlinear System ◽  
Asymptotic Stability ◽  
Carrying Capacity ◽  
Competitive Exclusion ◽  
Logistic Growth ◽  
Limited Growth ◽  
Growth Functions

A competitive mathematical model for the growth of two species is considered in this study. The main goal of the present study is to investigate the roles of two different growth functions: the logistic growth and the food limited growth. We established the main results that determine the asymptotic stability of semi-trivial as well as the coexistence solutions. If higher carrying capacity is embodied for the population following logistic growth then competitive exclusion of a food limited population is imminent and vice versa.GANIT J. Bangladesh Math. Soc.Vol. 37 (2017) 111-119

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