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Abstract

This paper proposes a method for exponential m-stability analysis of stochastic switched systems. The models, in a finite set of models, are non-linear stochastic models. It is assumed that there is no jump in the state at switching instants and there is no Zeno behaviour, ie, there is finite number of switches on every bounded interval. The stochastic hybrid systems have wide applications: transmission control protocol flows with congestion avoidance and slow-start modes; estimation in distributed networked systems; air traffic control; process control and communication networks for control systems. For analysis of stochastic switched system the multiple Lyapunov functions are used and exponential m-stability is proved. From the main result of the paper: 1) the exponential m₁ -stability of stochastic switched systems whereby m₁ ∈ (0, m); 2) the stability in probability. The exponentially stable equilibrium of system is relevant for practice because such systems are robust to perturbations.

Keywords

Exponential stability family of models multiple Lyapunov functions stochastic switched systems.

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References

Afanasev, V.N. , Kolmanovskij, V.B. and Nosov, V.P. 1989: Mathematical theory for control systems design. Vishaja Skola.

Cassandras, C.G. and Lafortune, S. 2008: Introduction to discrete event systems. Springer-Verlag.

Chatterjee, D. and Liberzon, D. 2004: On stability of stochastic switched systems. CDC 4, 4125-27.

Costa, O.I.V. , Fragoso, M.D. and Marques, R.P. 2005: Discrete-time Markov jump linear systems. Springer-Verlag.

Davis, M.H.A. 1993: Markov processes and optimization. Chapman and Hall.

Filipovic, V.Z. 2007: Robust control of constrained systems over a communication network with queues. International Conference on Control Systems and Computer Sciences.

Gihman, I.I. , Skorohod, A.V. and Jadrenko, M.I. 1988: Probability theory and mathematical statistics. Visha Skola.

Glover, W. and Lygeros, J. 2004: A stochastic hybrid model for air traffic control simulation . In Alur, R. and Pappas, G. , editors. Hybrid systems: computation and control. Springer Verlag.

Hespanaha, J.P. 2005: A model for stochastic hybrid systems with application to communication networks. Nonlinear Analysis 62, 1353-89.

10.

Hu, J. , Lygeros, J. and Sastry, S. 2000: Towards a theory of stochastic hybrid systems. In Lynch, N. and Krogh, B.H. , editors. Hybrid systems: computation and control. Springer-Verlag, 79-95.

11.

Isidori, A. 1999: Nonlinear control systems II. Springer-Verlag .

12.

Liberzon, D. 2003: Switching in systems and control. Birkhauser.

13.

Oksendal, B. 2000: Stochastic differential equations. An introduction with applications. fifth edition. Springer-Verlag.

14.

Oh, S. and Sastry, S. 2007: Approximate estimation of distributed networked control systems. American Control Conference, 987-1002 .

15.

Oksendal, B. and Sulem, A. 2005: Applied stochastic control of jump diffusions. Springer-Verlag.

16.

Pola, G. , Bujorianu, M.L. , Ligeros, J. and Benedetto, M.D.D. 2003: Stochastic hybrid models. An overview. IFAC Conference on Analysis and Design of Hybrid Systems.

Exponential stability of stochastic switched systems

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