Corpus ID: 7625386

Sub-homogeneous positive monotone systems are insensitive to heterogeneous time-varying delays

@article{Feyzmahdavian2014SubhomogeneousPM,
  title={Sub-homogeneous positive monotone systems are insensitive to heterogeneous time-varying delays},
  author={Hamid Reza Feyzmahdavian and Themistoklis Charalambous and Mikael Johansson},
  journal={ArXiv},
  year={2014},
  volume={abs/1407.1502}
}
We show that a sub-homogeneous positive monotone system with bounded heterogeneous time-varying delays is globally asymptotically stable if and only if the corresponding delay-free system is globally asymptotically stable. The proof is based on an extension of a delay-independent stability result for monotone systems under constant delays by Smith to systems with bounded heterogenous time-varying delays. Under the additional assumption of positivity and sub-homogenousvector fields, we establish… Expand

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References

SHOWING 1-10 OF 46 REFERENCES
Asymptotic Stability and Decay Rates of Homogeneous Positive Systems With Bounded and Unbounded Delays
TLDR
It is shown that global asymptotic stability of such systems is independent of the magnitude and variation of the time delays and bounds the decay rate of a significant class of nonlinear positive systems which includes positive linear systems as a special case. Expand
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
L∞-gain analysis for positive systems with distributed delays
TLDR
This paper addresses the L ∞ -gain analysis problem of positive linear systems with distributed delays by virtue of the positivity and linearity of the system, and presents a necessary and sufficient condition of an asymptotically stable positive system with distributed delay via linear programming. 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
D-Stability and Delay-Independent Stability of Homogeneous Cooperative Systems
We introduce a nonlinear definition of D-stability, extending the usual concept for positive linear time-invariant systems. We show that globally asymptotically stable, cooperative 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 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
Diagonal Lyapunov-Krasovskii functionals for discrete-time positive systems with delay
TLDR
The existence of a diagonal functional is necessary and sufficient for delay-independent stability of a positive linear time-delay system and conditions for the existence of diagonal L–K functionals for classes of nonlinear positive time- delay systems, which are not necessarily order preserving. Expand
...
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3
4
5
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