This chapter presents the fundamental results which underpin the theoretical analysis presented in this book. Lipschitz functions, comparison functions, Lyapunov stability theory including uniform ultimate boundedness, the Razumikhin theorem, linear output sliding surface design, and the geometric structure of nonlinear systems are covered. Some preliminary mathematical results developed by the authors are also provided.
CITATION STYLE
Yan, X. G., Spurgeon, S. K., & Edwards, C. (2017). Mathematical background. In Communications and Control Engineering (pp. 27–41). Springer International Publishing. https://doi.org/10.1007/978-3-319-48962-9_2
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