Asymptotic Stability and Decay Rates of Homogeneous Positive Systems With Bounded and Unbounded Delays

@article{Feyzmahdavian2014AsymptoticSA,
  title={Asymptotic Stability and Decay Rates of Homogeneous Positive Systems With Bounded and Unbounded Delays},
  author={Hamid Reza Feyzmahdavian and Themistoklis Charalambous and Mikael Johansson},
  journal={SIAM J. Control. Optim.},
  year={2014},
  volume={52},
  pages={2623-2650}
}
There are several results on the stability of nonlinear positive systems in the presence of time delays. However, most of them assume that the delays are constant. This paper considers time-varying, possibly unbounded, delays and establishes asymptotic stability and bounds the decay rate of a significant class of nonlinear positive systems which includes positive linear systems as a special case. Specifically, we present a necessary and sufficient condition for delay-independent stability of… Expand
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References

SHOWING 1-10 OF 95 REFERENCES
Asymptotic stability and decay rates of positive linear systems with unbounded delays
TLDR
This paper provides a set of easily verifiable necessary and sufficient conditions for delay-independent stability of positive linear systems subject to a general class of heterogeneous time-varying delays and demonstrates that the best bound on the decay rate can be found via convex optimization. Expand
Exponential Stability of Homogeneous Positive Systems of Degree One With Time-Varying Delays
TLDR
A set of conditions for establishing delay-independent stability and bounding the decay rate of a significant class of nonlinear positive systems which includes positive linear systems as a special case is presented. Expand
On the rate of convergence of continuous-time linear positive systems with heterogeneous time-varying delays
TLDR
A sufficient condition for delay-independent exponential stability of general linear systems is derived and an explicit expression that bounds the decay rate of the system is presented, demonstrating that the best decay rate that the bound can guarantee can be easily found via convex optimization techniques. Expand
Relationships between asymptotic stability and exponential stability of positive delay systems
TLDR
If a positive system is asymptotically stable for a given constant delay, then it is exponentially stable for all constant delays, and if the involved delays are unbounded, then the positive system may be not exponentially stable even if it is asylptotic stable. Expand
Sub-homogeneous positive monotone systems are insensitive to heterogeneous time-varying delays
TLDR
If the system has a unique equilibrium point in the positive orthant, it is proved that the stability test is necessary and sufficient and a novel test for global asymptotic stability is derived. Expand
Stability Analysis of Positive Switched Linear Systems With Delays
  • Xingwen Liu, C. Dang
  • Mathematics, Computer Science
  • IEEE Transactions on Automatic Control
  • 2011
TLDR
Under certain conditions, several stability results are established by constructing a sequence of functions that are positive, monotonically decreasing, and convergent to zero as time tends to infinity (additionally continuous for continuous-time systems). Expand
Stability Analysis of Positive Systems With Bounded Time-Varying Delays
TLDR
It turns out that, for any bounded time-varying delays, the magnitude of the delays does not affect the stability of these systems and system stability is completely determined by the system matrices. Expand
Stability Analysis for Continuous-Time Positive Systems With Time-Varying Delays
TLDR
It is shown that such a system is asymptotically stable for any continuous and bounded delay if and only if the sum of all the system matrices is a Hurwitz matrix. Expand
Power-Rate Global Stability of Dynamical Systems With Unbounded Time-Varying Delays
  • Tianping Chen, Lili Wang
  • Mathematics, Computer Science
  • IEEE Transactions on Circuits and Systems II: Express Briefs
  • 2007
TLDR
Under mild conditions, it is proved that the dynamical systems with unbounded time-varying delays are globally power stable. Expand
Stability of Positive Differential Systems With Delay
  • P. H. A. Ngoc
  • Mathematics, Computer Science
  • IEEE Transactions on Automatic Control
  • 2013
We first prove an explicit criterion for positive linear time-varying differential systems with distributed delay. Then some simple criteria for exponential stability of positive linearExpand
...
1
2
3
4
5
...