TITLE: Introduction to stochastic control
QUESTION [8 upvotes]: I'm looking for an introductory text on stochastic control. Any suggestions?

REPLY [5 votes]: I would also recommend the following two books of Kushner which provide a general and rigorous treatment of various topics in stochastic control theory including Lyapunov stability theory:

H.J. Kushner, Introduction to Stochastic Control, Holt, Rinehart and Winston Editions, 1971.
H.J. Kushner, Stochastic stability and control, Academic Press, New York, 1967.

From the point of view of stochastic programming, I would recommend the following references:

A. Shapiro, D. Dentcheva and A.Ruszczynski, Lectures on stochastic programming - modeling and theory, MPS-SIAM series on optimization, 2009.
D.P. Bertsekas and S.E. Shreve, Stochastic optimal control: the
discrete time case, Academic press, 1978.

The lecture notes by Shapiro et al. offers a very well-written and comprehensible on stochastic programming. The book of Bertsekas and Shreve provides a very careful and rigorous discussion of dynamic programming for discrete-time stochastic optimal control problems.
If you are interested in the special case of discrete-time Markovian systems, I would recommend:

O.L.V. Costa, M.D. Fragoso and R.P. Marques, Discrete-time Markov Jump Linear Systems, Springer 2005.

This books focuses on discrete-time Markov jump linear systems and discusses various notions of stochastic stability (e.g., mean square stability and almost sure convergence).
I would also recommend the book of Åström - I think it may be a good starting point.