Linear Stochastic Systems, originally published in 1988, is today as comprehensive a reference to the theory of linear discrete-time-parameter systems as ever. Its most outstanding feature is the unified presentation, including both input-output and state space representations of stochastic linear systems, together with their interrelationships.

The author first covers the foundations of linear stochastic systems and then continues through to more sophisticated topics including:

the fundamentals of stochastic processes and the construction of stochastic systems;
an integrated exposition of the theories of prediction, realization (modeling), parameter estimation, and control; and
a presentation of stochastic adaptive control theory.

Written in a clear, concise manner and accessible to graduate students, researchers, and teachers, this classic volume also includes background material to make it self-contained and has complete proofs for all the principal results of the book. Furthermore, this edition includes many corrections of errata collected over the years.

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Peter E. Caines received his BA in mathematics from Oxford University in 1967 and PhD in systems and control theory in 1970 from Imperial College, University of London, under the supervision of David Q. Mayne, FRS. After periods as a postdoctoral researcher and faculty member at UMIST, Stanford, UC Berkeley, Toronto, and Harvard, he joined McGill University, Montreal, in 1980, where he is James McGill Professor and Macdonald Chair in the Department of Electrical and Computer Engineering. He was a Fellow of CIFAR; is a Fellow of the IEEE, SIAM, and the Institute of Mathematics and Its Applications (UK); and was elected to the Royal Society of Canada in 2003. In 2009 he received the IEEE Control Systems Society Bode Lecture Prize. He is a member of Professional Engineers Ontario and a Senior Editor of Nonlinear Analysis: Hybrid Systems; his research interests include stochastic, multi-agent, mean field game, and hybrid systems theory, together with their applications to natural and artificial systems.

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