STABILITY OF LINEAR SYSTEMS WITH MARKOVIAN JUMPS - Mayta Guillermo, Jorge Enrique (2016)
In this work we will analyze the stability of linear systems governed by a Markov chain, this family is known in the specialized literature as linear systems with Markov jumps or by its acronyms in English MJLS as it is denoted in [1]. Linear systems governed by a Markov chain are dynamic systems with abrupt changes. We give some denitions of stability for the MJLS system, where these types of stability are equivalent as long as the state space of the Markov chain is finite.Finally we present a theorem that characterizes the stochastic stability by means of an equation of the Lyapunov type. The result is a generalization of a theorem in classical theory.