Stability criteria for linear time-invariant systems with point delays based on one-dimensional Routh–Hurwitz tests

2007 ◽  
Vol 187 (2) ◽  
pp. 1199-1207 ◽  
Author(s):  
M. De la Sen
Keyword(s):  
Linear Time ◽  
Stability Criteria ◽  
One Dimensional ◽  
Linear Time Invariant ◽  
Linear Time Invariant Systems ◽  
Time Invariant ◽  
Point Delays

scholarly journals On the links between limit characteristic zeros and stability properties of linear time-invariant systems with point delays and their delay-free counterparts

2004 ◽  
Vol 2004 (4) ◽  
pp. 339-357
Author(s):  
M. De La Sen ◽  
J. Jugo
Keyword(s):  
Analytic Functions ◽  
Linear Time ◽  
System Stability ◽  
Stable Region ◽  
Finite Characteristic ◽  
Free System ◽  
Linear Time Invariant ◽  
Linear Time Invariant Systems ◽  
Time Invariant ◽  
Point Delays

We investigate the relationships between the infinitely many characteristic zeros (or modes) of linear systems subject to point delays and their delay-free counterparts based on algebraic results and theory of analytic functions. The cases when the delay tends to zero or to infinity are emphasized in the study. It is found that when the delay is arbitrarily small, infinitely many of those zeros are located in the stable region with arbitrarily large modulus, while their contribution to the system dynamics becomes irrelevant. The remaining finite characteristic zeros converge to those of the delay-free nominal system. When the delay tends to infinity, infinitely many zeros are close to the origin. Furthermore, there exist two auxiliary delay-free systems which describe the relevant dynamics in both cases for zero and infinite delays. The maintenance of the delay-free system stability in the presence of sufficiently small delayed dynamics is also discussed in light ofH∞-theory. The main mathematical arguments used to derive the results are based on the theory of analytic functions.

scholarly journals Positivity and Stability of the Solutions of Caputo Fractional Linear Time-Invariant Systems of Any Order with Internal Point Delays

2011 ◽  
Vol 2011 ◽  
pp. 1-25 ◽  
Author(s):  
M. De la Sen
Keyword(s):  
Dynamic Systems ◽  
Linear Time ◽  
Asymptotic Properties ◽  
Linear Time Invariant ◽  
Nonnegative Solutions ◽  
Fractional Differential ◽  
Linear Time Invariant Systems ◽  
The Stability ◽  
Time Invariant ◽  
Point Delays

This paper is devoted to the investigation of the nonnegative solutions and the stability and asymptotic properties of the solutions of fractional differential dynamic systems involving delayed dynamics with point delays. The obtained results are independent of the sizes of the delays.

Sign in / Sign up

Export Citation Format

Share Document