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Stochastic systems for engineers. Modelling, estimation and control. (English) Zbl 0759.93070

New York: Prentice Hall. ix, 290 p. (1992).
This is a book with a very wide scope ranging from rudiments of probability theory to optimal control of stochastic systems. Its wide scope is both an asset and a liability: it includes a great amount of important information, however, no topic could be covered in depth. That is why it can be used quite successfully as a reference book but when it is intended for use as a graduate textbook, the derivations and proofs of almost all the results should be provided by the instructor.
Chapters 1 and 2 are on random variables and stochastic processes. Starting with the relative frequency interpretation of probability, the author thoroughly reviews the material on probability an stochastic processes needed later. This review includes independent increment processes, Ito integral, and models of continuous-time stochastic systems also.
Chapter 3 is devoted to the analysis of discrete-time and sampled-data systems. Chapter 4 is a natural follow-up on numerical methods for simulation of stochastic systems and computer aided analysis using fast Fourier transforms.
Chapter 5 covers continuous and discrete-time Kalman fittering with practical application considerations. Chapter 6 starts with minimum variance control and then presents control of deterministic and stochastic linear systems in a quadratically optimal fashion.
This book has five appendices respectively on complex transforms and linear systems, Butterworth filter design, counting and statistics, delta functions, and Riemann and Stieltjes integrals. Also, the solutions to the numerical exercises in the first three chapters are provided. In general, this book contains a fine collection of some of the most useful techniques in stochastic control and estimation.

MSC:

93E03 Stochastic systems in control theory (general)
93-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to systems and control theory
93E11 Filtering in stochastic control theory
93E20 Optimal stochastic control
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