This will be the most up-to-date book in the area (the closest competition was published in 1990)
This book takes a new slant and is in discrete rather than continuous time

Safety critical and high-integrity systems, such as industrial plants and economic systems can be subject to abrupt changes - for instance due to component or interconnection failure, and sudden environment changes etc.

Combining probability and operator theory, Discrete-Time Markov Jump Linear Systems provides a unified and rigorous treatment of recent results for the control theory of discrete jump linear systems, which are used in these areas of application.

The book is designed for experts in linear systems with Markov jump parameters, but is also of interest for specialists in stochastic control since it presents stochastic control problems for which an explicit solution is possible - making the book suitable for course use.

From the reviews:

"This text is very well written...it may prove valuable to those who work in the area, are at home with its mathematics, and are interested in stability of linear systems, optimal control, and filtering." Journal of the American Statistical Association, December 2005

Most up-to-date book in the area Combines probability and operator theory to provide a unified and rigorous treatment of recent results Takes a new approach using discrete rather than continuous time Includes supplementary material: sn.pub/extras

Inhalt
Preface.- Markovian Jump Linear Systems.- Background Material.- On Stability.- Optimal Control.- Linear Filtering.- Quadratic Optimal Control with Partial Information.- H2- Control.- Design Techniques and Examples.- Appendix A: Coupled Algebraic Riccati Equations.- Appendix B: Auxiliary Results for the Linear Filtering Problem with (k) Unknown.- Appendix C: Auxiliary Results for the H2 Control Problem.- Notation and Corrections.- References.