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This book is devoted to one of the fastest developing fields in modern control theory - the so-called H-infinity optimal control theory. Th can be used for a second or third year graduate level course in the subject, and researchers working in the area will find th useful as a standard reference. Based mostly on recent work of the authors, th is written on a good mathematical level. Many results in it are original, interesting, and inspirational. The topic is central to modern control and hence this definitiv is highly recommended to anyone who wishes to catch up with important theoretical developments in applied mathematics and control.