scholarly journals Uniformly asymptotic stability of second-order linear time-varying systems

2020 ◽  
Vol 12 (9) ◽  
pp. 168781402095509
Author(s):  
Da-Ke Gu ◽  
Chao Lu
Keyword(s):  
Asymptotic Stability ◽  
Stability Criterion ◽  
Linear Time ◽  
Second Order ◽  
State Feedback Control ◽  
Time Varying ◽  
Order Linear ◽  
Time Varying Systems ◽  
Uniformly Asymptotic Stability ◽  
The Stability

This paper is concerned with the stability of second-order linear time-varying systems. By utilizing the Lyapunov approach, a generally uniformly asymptotic stability criterion is obtained by adding the system matrices into the quadratic Lyapunov candidate function. In the case of the derivative of the Lyapunov candidate function is semi-positive definite, the stability criterion is also efficient. Based on the proposed results, the systems with uncertain disturbances such as structured independent and structured dependent perturbations are considered. Using the matrix measure and the singular value theory, the bounds of the uncertainties are obtained that guarantee the system uniformly asymptotically stable, while the bounds of state feedback control input are also derived to stabilize the second-order linear time-varying systems. Finally, several numerical examples are given to prove the validity and correctness of the proposed criteria with existing ones.

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

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.

On the Stability of Second Order Time Varying Linear Systems

2005 ◽  
Vol 128 (3) ◽  
pp. 408-410 ◽  
Author(s):  
M. Tadi
Keyword(s):  
Asymptotic Stability ◽  
Linear Systems ◽  
Stiffness Matrix ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Second Order ◽  
Time Varying ◽  
The Stability ◽  
Second Order Systems

This note considers the stability of linear time varying second order systems. It studies the case where the stiffness matrix is a function of time. It provides sufficient conditions for stability and asymptotic stability of the system provided that certain conditions on the stiffness matrix are satisfied.

scholarly journals Inverse Commutativity Conditions for Second-Order Linear Time-Varying Systems

2017 ◽  
Vol 2017 ◽  
pp. 1-6 ◽  
Author(s):  
Mehmet Emir Koksal
Keyword(s):  
Differential Equation ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Second Order ◽  
Necessary And Sufficient Conditions ◽  
Time Varying ◽  
Order Linear ◽  
Time Varying Systems ◽  
Initial States ◽  
Necessary And Sufficient

The necessary and sufficient conditions where a second-order linear time-varying system A is commutative with another system B of the same type have been given in the literature for both zero initial states and nonzero initial states. These conditions are mainly expressed in terms of the coefficients of the differential equation describing system A. In this contribution, the inverse conditions expressed in terms of the coefficients of the differential equation describing system B have been derived and shown to be of the same form of the original equations appearing in the literature.

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.

Sign in / Sign up

Export Citation Format

Share Document