# Finite-time stabilization for Markov jump systems governed by deterministic switches

@article{Zhao2014FinitetimeSF, title={Finite-time stabilization for Markov jump systems governed by deterministic switches}, author={Chongzhong Zhao and Xiaoli Luan and Fei Liu}, journal={IFAC Proceedings Volumes}, year={2014}, volume={47}, pages={11123-11128} }

Abstract The problem of controller synthesis in a fixed time interval for discrete-time switching Markov jump systems is dealt with in this paper. Compared with the existing results, the new proposed stabilization conditions are obtained by permitting the stochastic Lyapunov energy function to rise at each switching instant, but the switching signal is constraint by an average dwell time. Finally, the validity of the obtained results is demonstrated with an example.

#### References

SHOWING 1-10 OF 29 REFERENCES

Finite-time stability of linear time-varying systems with jumps

- Computer Science, Mathematics
- Autom.
- 2009

The paper provides a necessary and sufficient condition for finite-time stability, requiring a test on the state transition matrix of the system under consideration, and a sufficient condition involving two coupled differential-difference linear matrix inequalities. Expand

Finite-time stabilisation for Markov jump systems with Gaussian transition probabilities

- Mathematics
- 2013

The problems of finite-time analysis and design for a class of Markov jump systems with Gaussian transition probabilities (TPs) are investigated in this study. Gaussian TP density function is… Expand

On designing of sliding-mode control for stochastic jump systems

- Mathematics, Computer Science
- IEEE Transactions on Automatic Control
- 2006

Using Linear matrix inequalities (LMIs) approach, sufficient conditions are proposed to guarantee the stochastic stability of the underlying system and a reaching motion controller is designed such that the resulting closed-loop system can be driven onto the desired sliding surface in a limited time. Expand

Markov Jump Linear Systems with switching transition rates: Mean square stability with dwell-time

- Computer Science, Mathematics
- Autom.
- 2010

The stability of a class of Markov Jump Linear Systems characterized by piecewise-constant transition rates and system dynamics is investigated and it is shown that both the stability criteria admit an LMI implementation. Expand

Almost Sure Stability of Markov Jump Linear Systems With Deterministic Switching

- Computer Science, Mathematics
- IEEE Transactions on Automatic Control
- 2013

A class of linear systems whose piecewise-constant dynamic matrix is subject to both stochastic jumps, governed by a Markov chain, and deterministic switches is studied, dubbed switching dynamics Markov jump linear systems (SD-MJLS). Expand

Exponential l2–l∞ Control for Discrete-Time Switching Markov Jump Linear Systems

- Mathematics, Computer Science
- Circuits Syst. Signal Process.
- 2013

By resorting to the average dwell time approach, the mean square exponential stability criteria are presented with an exponential l2–l∞ performance index and a decay rate, and the corresponding controller is also designed. Expand

Stability and Stabilization of Continuous-Time Switched Linear Systems

- Mathematics, Computer Science
- SIAM J. Control. Optim.
- 2006

This paper addresses two strategies for the stabilization of continuous-time, switched linear systems and is designed from the solution of what the authors call Lyapunov-Metzler inequalities from which the stability condition (including chattering) is expressed. Expand

Finite-time control of discrete-time linear systems

- Computer Science, Mathematics
- IEEE Transactions on Automatic Control
- 2005

This note considers the finite-time stabilization of discrete-time linear systems subject to disturbances generated by an exosystem and finds some sufficient conditions for the existence of an output feedback controller guaranteeing finite- time stability. Expand

Finite-time stabilization by state feedback control for a class of time-varying nonlinear systems

- Engineering, Computer Science
- Autom.
- 2012

Finite-time stabilization is considered for a class of nonlinear systems dominated by a lower-triangular model with a time-varying gain based on the finite-time Lyapunov stability theorem and dynamic gain control design approach with gains being tuned online by two dynamic equations. Expand

Analysis and Synthesis of Markov Jump Linear Systems With Time-Varying Delays and Partially Known Transition Probabilities

- Mathematics, Computer Science
- IEEE Transactions on Automatic Control
- 2008

Sufficient conditions for stochastic stability of the underlying systems are derived via the linear matrix inequality (LMI) formulation, and the design of the stabilizing controller is further given. Expand