Reliable controllable sets for constrained Markov-Jump Linear Systems

Abstract

Robust λ-contractive sets have been proposed in previous literature for uncertain polytopic linear systems. It is well known that, if initial state is inside such sets, it is guaranteed to converge to the origin. This work presents the generalization of such concepts to systems whose behaviour changes among different linear models with probability given by a Markov chain. We propose sequence-dependent sets and associated controllers that can ensure a reliability bound when initial conditions are outside the maximal λ-contractive set. Such reliability bound will be understood as the probability of actually reaching the origin from a given initial condition without violating constraints. As initial conditions are further away from the origin, the likelihood of reaching the origin decreases.