This paper addresses the dynamic output feedback control problem of continu
ous-time Markovian jump linear systems. The fundamental point in the analys
is is an LMI characterization, comprising all dynamical compensators that s
tabilize the closed-loop system in the mean square sense. The H-2 and H-inf
inity-norm control problems are studied, and the H-2 and H-infinity filteri
ng problems are solved as a by product.