A less conservative stability test for second-order linear time-varying vector differential equations

2007 ◽  
Vol 80 (4) ◽  
pp. 523-526 ◽  
Author(s):  
J. Sun¶ ◽  
Q.-G. Wang ◽  
Q.-C. Zhong
Keyword(s):  
Differential Equations ◽  
Linear Time ◽  
Second Order ◽  
Stability Test ◽  
Time Varying ◽  
Order Linear

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 Decomposition of a second-order linear time-varying differential system as the series connection of two first order commutative pairs

2016 ◽  
Vol 14 (1) ◽  
pp. 693-704 ◽  
Author(s):  
Mehmet Emir Koksal
Keyword(s):  
Differential System ◽  
Linear Time ◽  
Second Order ◽  
Time Varying ◽  
Small Class ◽  
Direct Simulation ◽  
Explicit Formulas ◽  
Order Linear ◽  
Numerical Errors ◽  
First Order

AbstractNecessary and sufficiently conditions are derived for the decomposition of a second order linear time- varying system into two cascade connected commutative first order linear time-varying subsystems. The explicit formulas describing these subsystems are presented. It is shown that a very small class of systems satisfies the stated conditions. The results are well verified by simulations. It is also shown that its cascade synthesis is less sensitive to numerical errors than the direct simulation of the system itself.

scholarly journals On stability of linear time-varying second-order differential equations

2006 ◽  
Vol 64 (1) ◽  
pp. 137-151 ◽  
Author(s):  
Luu Hoang Duc ◽  
Achim Ilchmann ◽  
Stefan Siegmund ◽  
Peter Taraba
Keyword(s):  
Differential Equations ◽  
Linear Time ◽  
Second Order ◽  
Time Varying ◽  
Second Order Differential Equations

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.

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