# Exponential stability of stochastic delay interval systems with Markovian switching

@article{Mao2002ExponentialSO, title={Exponential stability of stochastic delay interval systems with Markovian switching}, author={Xuerong Mao}, journal={IEEE Trans. Autom. Control.}, year={2002}, volume={47}, pages={1604-1612} }

In the past few years, a lot of research has been dedicated to the stability of interval systems as well as the stability of systems with Markovian switching. However, little research has been on the stability of interval systems with Markovian switching, which is the topic of this paper. The system discussed is the stochastic delay interval system with Markovian switching. It is a very advanced system and takes all the features of interval systems, Ito equations, and Markovian switching, as…

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## References

SHOWING 1-10 OF 26 REFERENCES

Stochastic differential delay equations with Markovian switching

- Mathematics
- 2000

Stochastic modelling has come to play an important role in many branches of science and industry. An area of particular interest has been the automatic control of stochastic systems, with consequent…

Stochastic Stability of Differential Equations

- Mathematics
- 1980

Boundedness in Probability and Stability of Stochastic Processes Defined by Differential Equations.- 2.Stationary and Periodic Solutions of Differential Equations. 3.Markov Processes and Stochastic…

Jump linear systems in automatic control

- Mathematics
- 1990

This book is a monograph on hybrid parameter processes that are characterized by the presence of a discrete parameter and continuous variables. The author considers stochastic models in which the…

Sufficient Conditions for the Stability of Interval Systems with Multiple Time-Varying Delays

- Mathematics
- 1997

Abstract In this paper, the global asymptotic stability of interval systems with multiple unknown time-varying delays is considered. Some criteria are derived to guarantee the global asymptotic…

Stability of a Random diffusion with linear drift

- Mathematics
- 1996

We consider a linear system with Markovian switching which is perturbed by Gaussian type noise. If the linear system is mean square stable then we show that under certain conditions the perturbed…

Controllability, stabilizability, and continuous-time Markovian jump linear quadratic control

- Mathematics
- 1990

Consideration is given to the control of continuous-time linear systems that possess randomly jumping parameters which can be described by finite-state Markov processes. The relationship between…

Optimal choice of time-scaling factor for linear system approximations using Laguerre models

- Mathematics, Computer ScienceIEEE Trans. Autom. Control.
- 1994

A direct application of Clowes' result is able to obtain approximations for irrational transfer functions which minimize the frequency domain error in the L/sub 2/ sense.

Necessary and sufficient conditions for the Hurwitz and Schur stability of interval matrices

- MathematicsIEEE Trans. Autom. Control.
- 1994

The authors develop an algorithm to determine the Hurwitz and the Schur stability properties of interval matrices and relate the above results to the existence of quadratic Lyapunov functions for linear time-invariant systems with interval-valued coefficient matrices.