Duality Between Invariant Spaces for Max-Plus Linear Discrete Event Systems
Michael Di Loreto, Stéphane Gaubert, Ricardo D. Katz, Jean-Jacques Loiseau · SIAM Journal on Control and Optimization · 2010
We extend the notions of conditioned and controlled invariant spaces to linear dynamical systems over the max-plus or tropical semiring. We establish a duality theorem relating both notions, which we use to construct dynamic observers. These are useful in situations in which some of the system coefficients may vary within certain intervals. The results are illustrated by an application to a manufacturing system.