An Integral Method of Liapunov Function Generation for Nonlinear Autonomous Systems

1965 ◽  
Vol 32 (3) ◽  
pp. 569-575 ◽  
Author(s):  
J. A. Walker ◽  
L. G. Clark
Keyword(s):  
Asymptotic Stability ◽  
Integral Method ◽  
Autonomous Systems ◽  
Liapunov Function ◽  
Higher Order ◽  
Phase Variable ◽  
Variable Form ◽  
Function Generation ◽  
Liapunov Functions

A method is developed for generating Liapunov functions with which to determine the domain of asymptotic stability for nonlinear autonomous systems of any order, so long as these systems may be represented in phase variable form. The method is illustrated by several examples of higher order.

Limit Cycles of Higher Order Nonlinear Autonomous Systems

1971 ◽  
Vol 291 (3) ◽  
pp. 195-210 ◽  
Author(s):  
R.K. Jonnada ◽  
C.N. Weygandt
Keyword(s):  
Limit Cycles ◽  
Autonomous Systems ◽  
Higher Order

Recursive Lyapunov Functions

1989 ◽  
Vol 111 (4) ◽  
pp. 641-645 ◽  
Author(s):  
Andrzej Olas
Keyword(s):  
Asymptotic Stability ◽  
Lyapunov Function ◽  
Exponential Stability ◽  
Performance Measures ◽  
Lyapunov Functions ◽  
Stability Problem ◽  
Autonomous Systems ◽  
Sequence Of Functions

The paper presents the concept of recursive Lyapunov function. The concept is applied to investigation of asymptotic stability problem of autonomous systems. The sequence of functions {Uα(i)} and corresponding performance measures λ(i) are introduced. It is proven that λ(i+1) ≤ λ(i) and in most cases the inequality is a strong one. This fact leads to a concept of a recursive Lyapunov function. For the very important applications case of exponential stability the procedure is effective under very weak conditions imposed on the function V = U(0). The procedure may be particularly applicable for the systems dependent on parameters, when the Lyapunov function determined from one set of parameters may be employed at the first step of the procedure.

scholarly journals Normative Epistemology for Lethal Autonomous Weapons Systems

2021 ◽  
pp. 237-258
Author(s):  
S. Kate Devitt
Keyword(s):  
Autonomous Systems ◽  
Higher Order ◽  
International Humanitarian Law ◽  
Humanitarian Law ◽  
Ethical Justification ◽  
Autonomous Weapons ◽  
Development Evaluation ◽  
Normative Epistemology ◽  
Weapons Systems

The rise of human-information systems, cybernetic systems, and increasingly autonomous systems requires the application of epistemic frameworks to machines and human-machine teams. This chapter discusses higher-order design principles to guide the design, evaluation, deployment, and iteration of Lethal Autonomous Weapons Systems (LAWS) based on epistemic models. Epistemology is the study of knowledge. Epistemic models consider the role of accuracy, likelihoods, beliefs, competencies, capabilities, context, and luck in the justification of actions and the attribution of knowledge. The aim is not to provide ethical justification for or against LAWS, but to illustrate how epistemological frameworks can be used in conjunction with moral apparatus to guide the design and deployment of future systems. The models discussed in this chapter aim to make Article 36 reviews of LAWS systematic, expedient, and evaluable. A Bayesian virtue epistemology is proposed to enable justified actions under uncertainty that meet the requirements of the Laws of Armed Conflict and International Humanitarian Law. Epistemic concepts can provide some of the apparatus to meet explainability and transparency requirements in the development, evaluation, deployment, and review of ethical AI.

scholarly journals On (h0,h)-stability of autonomous systems

1992 ◽  
Vol 5 (4) ◽  
pp. 331-337 ◽  
Author(s):  
Xinzhi Liu
Keyword(s):  
Asymptotic Stability ◽  
Autonomous System ◽  
Autonomous Systems ◽  
Qualitative Behavior ◽  
Initial Values

In this paper, we discuss the qualitative behavior of a map h along solutions of an autonomous system whose initial values are measured by a second map h0. By doing this, we may deal with, in a unified way, several concepts and associated problems, which are usually considered separately. Five theorems on asymptotic stability are given and two examples are worked out.

Synthesis of Harmonic Motion Generating Linkages: Part II — Path and Motion Generation

1987 ◽  
Author(s):  
K. Farhang ◽  
A. Midha ◽  
A. S. Hall
Keyword(s):  
Companion Paper ◽  
Higher Order ◽  
Rate Of Change ◽  
Connecting Rod ◽  
Motion Generation ◽  
Harmonic Motion ◽  
Function Generation ◽  
Synthesis Techniques ◽  
General Synthesis

Abstract This paper, a sequel to a companion paper on function generation, discusses the path and motion generation problems in the synthesis of linages with relatively small input cranks. The point on the floating link (i.e., the coupler of a crank-rocker linkage point on connecting rod in a slider-crank linkage) traces an approximate ellipse. This fact serves as a major distinction between the method described herein and the conventional, more general, synthesis techniques. In other words, only elliptical paths may be generated by the path (or coupler) points in the synthesis of linkages with small cranks. Higher order path and motion generation, in which velocity, acceleration, slope and the rate of change of slope of the coupler path may be specified, are also addressed in this paper.

scholarly journals A Novel Method to Determine the Local Stability of the n-Species Lotka-Volterra System with Multiple Delays

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Xiao-Ping Chen ◽  
Hao Liu
Keyword(s):  
Asymptotic Stability ◽  
Local Stability ◽  
Integral Method ◽  
Numerical Experiments ◽  
Positive Equilibrium ◽  
Multiple Delays ◽  
Volterra System ◽  
Local Asymptotic Stability ◽  
Discrete Delays ◽  
Novel Method

The n-species Lotka-Volterra system with discrete delays is considered. The local asymptotic stability of positive equilibrium is investigated based on a contour integral method. The main purpose of this paper is to propose a new and general algorithm to study the local asymptotic stability of the positive equilibrium for then-dimensional Lotka-Volterra system. Some numerical experiments are carried out to show the effectiveness of the proposed method.

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