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Published in:
2018 | OriginalPaper | Chapter
3. Mathematical Preliminaries
Author : Nhan T. Nguyen
Published in: Model-Reference Adaptive Control
Publisher: Springer International Publishing
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Abstract
This chapter presents some basic mathematical fundamentals for adaptive control theory. Vector and matrix norms are defined. The existence and uniqueness of a solution of a nonlinear differential equation are stated by the Cauchy theorem and the Lipschitz condition. Positive-valued functions are an important class of functions in adaptive control theory. Positive definiteness of a real-valued function is defined. The properties of a positive-definite matrix are given.