# EECI09: Jump linear Markov processes

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In this lecture, we give a brief overview of Markovian jump linear systems. Such systems display multiple linear modes for the evolution of the state, and the modes are chosen stochastically. Such systems were important in the early development of networked control systems, where the communication channels were modeled as a Markov chain for effects such as delay and packet loss. As we will see in the next chapter, the one-block design problem for such systems can be studied in the framework of Markovian jump linear systems.

## Lecture Materials

- Lecture slides: Summary

## Further Reading

Discrete-Time Markov Jump Linear Systems (Probability and its Applications), O.L.V. Costa, M.D. Fragoso, and R.P. Marques. Springer, 2004. This book is a good introduction to Markov jump linear systems.

On a Stochastic Sensor Selection Algorithm with Applications in Sensor Scheduling and Sensor Coverage, V. Gupta, T. Chung, B. Hassibi and R. M. Murray, Automatica, 42(2):251-260, February 2006. This paper presents the necessary and sufficient stability conditions for the estimation problem. The results for the LQR problem are dual to the results obtained here.

Real-Time Control Systems with Delays, J. Nilsson, Ph.D. Thesis, Department of Automatic Control, Lund University, 1998. This thesis extends the Markovian jump linear system framework to the case when the system mode defines a probability density function for the system matrices.

## Additional Information

- Networked Control Systems Repository (M. Branicky and S. Phillipps)
- 2008 lecture page
- Additional links to external information