scholarly journals On the Global Asymptotic Stability of Switched Linear Time-Varying Systems with Constant Point Delays

2008 ◽  
Vol 2008 ◽  
pp. 1-31 ◽  
Author(s):  
M. de la Sen ◽  
A. Ibeas
Keyword(s):  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Linear Time ◽  
Time Varying ◽  
System Matrix ◽  
Almost Everywhere ◽  
Time Varying Systems ◽  
The Matrix ◽  
Delayed System ◽  
Point Delays

This paper investigates the asymptotic stability of switched linear time-varying systems with constant point delays under not very stringent conditions on the matrix functions of parameters. Such conditions are their boundedness, the existence of bounded time derivatives almost everywhere, and small amplitudes of the appearing Dirac impulses where such derivatives do not exist. It is also assumed that the system matrix for zero delay is stable with some prescribed stability abscissa for all time in order to obtain sufficiency-type conditions of asymptotic stability dependent on the delay sizes. Alternatively, it is assumed that the auxiliary system matrix defined for all the delayed system matrices being zero is stable with prescribed stability abscissa for all time to obtain results for global asymptotic stability independent of the delays. A particular subset of the switching instants is the so-called set of reset instants where switching leads to the parameterization to reset to a value within a prescribed set.

scholarly journals On the Uniform Exponential Stability of Time-Varying Systems Subject to Discrete Time-Varying Delays and Nonlinear Delayed Perturbations

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Maher Hammami ◽  
Mohamed Ali Hammami ◽  
Manuel De la Sen
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Discrete Time ◽  
Global Asymptotic Stability ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Uniform Exponential Stability ◽  
Time Varying Systems ◽  
Delayed Time

This paper addresses the problem of stability analysis of systems with delayed time-varying perturbations. Some sufficient conditions for a class of linear time-varying systems with nonlinear delayed perturbations are derived by using an improved Lyapunov-Krasovskii functional. The uniform global asymptotic stability of the solutions is obtained in terms of convergence toward a neighborhood of the origin.

Asymptotic Stability of Second-Order Linear Time-Varying Systems

2006 ◽  
Vol 29 (6) ◽  
pp. 1472-1476 ◽  
Author(s):  
Ryotaro Okano ◽  
Takashi Kida ◽  
Tomoyuki Nagashio
Keyword(s):  
Asymptotic Stability ◽  
Linear Time ◽  
Second Order ◽  
Time Varying ◽  
Order Linear ◽  
Time Varying Systems

scholarly journals Data-Driven Networked Optimal Iterative Learning Control for Discrete Linear Time-Varying Systems with One-Operation Bernoulli-Type Communication Delays

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Yan Geng ◽  
Xiaoe Ruan ◽  
Hyo-Sung Ahn
Keyword(s):  
Iterative Learning Control ◽  
Linear Time ◽  
Tracking Error ◽  
Learning Control ◽  
Iterative Learning ◽  
Data Driven ◽  
Time Varying ◽  
Communication Delays ◽  
System Matrix ◽  
Time Varying Systems

This paper develops a type of data-driven networked optimal iterative learning control strategy for a class of discrete linear time-varying systems with one-operation Bernoulli-type communication delays. In terms of the stochastic Bernoulli-type one-operation communication delayed inputs and outputs, the previous-iteration synchronous compensations are adopted. By means of deriving gradients of two types of objective functions that express the optimal approximation of the system matrix and the minimal tracking error, the strategy approximates the system matrix and upgrades the control inputs in an interact mode as the iteration evolves. By taking advantage of matrix theory and statistical technique, it is derived that the approximation discrepancy of the system matrix is bounded and the mathematical expectation of the tracking error vanishes as the iteration goes on. Numerical simulations manifest the validity and effectiveness.

A numerical sufficiency test for the asymptotic stability of linear time-varying systems

Automatica ◽  
2007 ◽  
Vol 43 (4) ◽  
pp. 631-638 ◽  
Author(s):  
Ph. Mullhaupt ◽  
D. Buccieri ◽  
D. Bonvin
Keyword(s):  
Asymptotic Stability ◽  
Linear Time ◽  
Time Varying ◽  
Time Varying Systems

Asymptotic Stabilization of Fractional Permanent Magnet Synchronous Motor

2017 ◽  
Vol 13 (2) ◽  
Author(s):  
Yuxiang Guo ◽  
Baoli Ma
Keyword(s):  
Nonlinear Dynamics ◽  
Asymptotic Stability ◽  
Permanent Magnet ◽  
Linear Time ◽  
Permanent Magnet Synchronous Motor ◽  
Synchronous Motor ◽  
Time Varying ◽  
Linear Time Invariant ◽  
Time Varying Systems ◽  
The Stability

This paper is mainly concerned with asymptotic stability for a class of fractional-order (FO) nonlinear system with application to stabilization of a fractional permanent magnet synchronous motor (PMSM). First of all, we discuss the stability problem of a class of fractional time-varying systems with nonlinear dynamics. By employing Gronwall–Bellman's inequality, Laplace transform and its inverse transform, and estimate forms of Mittag–Leffler (ML) functions, when the FO belongs to the interval (0, 2), several stability criterions for fractional time-varying system described by Riemann–Liouville's definition is presented. Then, it is generalized to stabilize a FO nonlinear PMSM system. Furthermore, it should be emphasized here that the asymptotic stability and stabilization of Riemann–Liouville type FO linear time invariant system with nonlinear dynamics is proposed for the first time. Besides, some problems about the stability of fractional time-varying systems in existing literatures are pointed out. Finally, numerical simulations are given to show the validness and feasibleness of our obtained stability criterions.

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