Set-stability for nonlinear systems

In this report we will give a treatment of important tools for analyzing stability in nonlinear dynamical systems. This inludes both stability of equilibria and the more general concept of set-stability. Some suggested applications for its use are time-varying systems, maneuvering systems (Skjetne et al.; 2004), adaptive systems, and observer designs. A variety of references are used where the most important are Lin (1992); Lin et al. (1995); Sontag and Wang (1995a); Lin et al. (1996); Teel and Praly (2000); Teel (2002); Khalil (2002). Most of the definitions and theorems are taken from the mentioned references and organized in a consistent notation. The proper citations are clearly referenced. Using these references a few theorems have been developed further by the author as minor extensions to the existing theory. This concerns in particular Theorem 4.3, published in Skjetne et al. (2005), and Theorem 5.2, published in Skjetne et al. (2004). NTNU report no.: 2004-8-W