  We study how physical measures vary with the underlying dynamics in the open
class of $C^r$, $r>1$, strong partially hyperbolic diffeomorphisms for which
the central Lyapunov exponents of every Gibbs $u$-state is positive. If
transitive, such a diffeomorphism has a unique physical measure that persists
and varies continuously with the dynamics.
  A main ingredient in the proof is a new Pliss-like Lemma which, under the
right circumstances, yields frequency of hyperbolic times close to one. Another
novelty is the introduction of a new characterization of Gibbs $cu$-states.
Both of these may be of independent interest.
  The non-transitive case is also treated: here the number of physical measures
varies upper semi-continuously with the diffeomorphism, and physical measures
vary continuously whenever possible.
