In this chapter, we introduce the main tools and principal results that play fundamental roles for the whole book, such as Lyapunov function, K-class function (or wedge function), Dini-derivative, M-matrix, Hurwitz matrix, positive (negative) definite matrix; and the principal theorems on global stability, partial global stability, and global stability of sets.
Partial materials presented in this chapter are due to Lyapunov [97], Hahn [38], Malkin [102] (Sect. 2.1), Yoshizawa [170] (Sect. 2.2), Rumyantsev [133, 134] (Sect. 2.4.2), Liao [68, 69] (Sect. 2.3-2.6), and Liao [69, 70] (Sect. 2.7 and 2.8).
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(2008). Principal Theorems on Global Stability. In: Absolute Stability of Nonlinear Control Systems. Mathematical Modelling: Theory and Applications, vol 25. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-8482-9_2
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