Some Forms of Globally Asymptotically Stable Attractors

This chapter is devoted to presenting some definitions and relevant results about some forms of globally asymptotically stable discrete time mappings and continuous time systems. In Sec. 8.2, we present the important definitions and results about the direct Lyapunov stability for ordinary differential equations. The necessary conditions for the exponential stability of nonlinear time-varying are presented in Sec. 8.3. In Sec. 8.4, we present and prove the Lasalle’s invariance principle. In Sec. 8.5, we present an overview about the extension of the direct Lyapunov method presented in Sec. 8.2 to systems of equations of perturbed motion with fractional-like derivatives.