Mathematical preliminaries

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.