Stability Analysis of Positive Semi-Markovian Jump Linear Systems with State Resets

@article{Ogura2014StabilityAO,
  title={Stability Analysis of Positive Semi-Markovian Jump Linear Systems with State Resets},
  author={Masaki Ogura and Clyde F. Martin},
  journal={SIAM J. Control. Optim.},
  year={2014},
  volume={52},
  pages={1809-1831}
}
This paper studies the mean stability of positive semi-Markovian jump linear systems. We show that their mean stability is characterized by the spectral radius of a matrix that is easy to compute. In deriving the condition we use a certain discretization of a semi-Markovian jump linear system that preserves stability. Also we show a characterization for the exponential mean stability of continuous-time positive Markovian jump linear systems. Numerical examples are given to illustrate the… 

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References

SHOWING 1-10 OF 41 REFERENCES

Stability of stochastic differential equations with Markovian switching

Stochastic stability properties of jump linear systems

Jump linear systems are defined as a family of linear systems with randomly jumping parameters (usually governed by a Markov jump process) and are used to model systems subject to failures or changes

Stochastic stability of jump linear systems

In this note, some testable conditions for mean square (i.e., second moment) stability for discrete-time jump linear systems with time-homogenous and time-inhomogenous finite state Markov chain form

Stochastic stability and robust stabilization of semi‐Markov jump linear systems

The semi‐Markov jump linear system (S‐MJLS) is more general than the Markov jump linear system (MJLS) in modeling some practical systems. Unlike the constant transition rates in the MJLS, the

Stability properties of reset systems

On the Stability of Switched Positive Linear Systems

TLDR
This note shows that the Hurwitz stability of the convex hull of a set of Metzler matrices is a necessary and sufficient condition for the asymptotic stability for the associated switched linear system under arbitrary switching.

Linear Copositive Lyapunov Functions for Continuous-Time Positive Switched Systems

TLDR
A complete characterization for the existence of a common linear copositive Lyapunov function for all the subsystems is provided and leads to a very easy checking procedure.

Co-Positive Lyapunov Functions for the Stabilization of Positive Switched Systems

TLDR
The results obtained in the first part of the paper are exploited to characterize exponential stabilizability of positive switched systems with delays, and to provide a description of all the “switched equilibrium points” of an affine positive switched system.