Stability of second-order multidimensional linear time-varying systems

1991 ◽  
Vol 14 (5) ◽  
pp. 1040-1045 ◽  
Author(s):  
Ping Hsu ◽  
Jinnwen Wu
Keyword(s):  
Linear Time ◽  
Second Order ◽  
Time Varying ◽  
Time Varying Systems ◽  
Multidimensional 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 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.

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.

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