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, 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. Oswaldo Luiz do Valle Costa is Professor in the Department of Telecommunications and Control Engineering at the University of São Paulo, Marcelo Dutra Fragoso is Professor in the Department of Systems and Control at the National Laboratory for Scientific Computing - LNCC/MCT, Rio de Janeiro, and Ricardo Paulino Marques works in the Department of Telecommunications and Control Engineering at the University of São Paulo.