Asymptotic Stability of 2-Switched Systems based on Lyapunov Functions

This paper examines a 2-switched system case study as an application of the ideas of global asymptotic stability developed in a number of previous papers. The idea here is to construct a globally attractive n-1-dimensional hyperspace having the property that the "average" system restricted on the hyperspace is stable. Definite quadratic Lyapunov functions are then constructed having energy-reducing regions whose intersection creates an "envelope" around the hyperspace for the 2-switched system to evolve in a stable fashion. Care is taken for the union of the energy-reducing regions to cover the state-space as well as satisfy certain theorems and conditions set forth in previous work.