Stability definitions

This is the first video lecture of ELE8088 where we give some important definitions: discrete-time dynamical systems, invariant sets, attractivity, stability, and K-infinity class functions. ▬ Contents ▬▬▬▬▬▬▬▬▬▬ 00:00 - Introduction 00:49 - Discrete-time systems 01:58 - Solutions/trajectories 02:38 - Equilibria 04:01 - Invariance 05:57 - Attractivity 07:42 - Lyapunov Stability 10:11 - Stability vs Attractivity 14:14 - GAS 14:38 - Global vs Local 17:15 - GES 19:08 - K-infinity 20:39 - Outro ▬ About ▬▬▬▬▬▬▬▬▬▬▬ This video is part of a series of video lectures on optimal control theory for the module "Control Estimation Theory," which is taught in the MSc in Electronics, at the School of Electronics, Electrical Engineering and Computer Science (EEECS) at Queen's University Belfast (see https://www.qub.ac.uk/courses/postgra.... The module is taught by Dr Pantelis Sopasakis.