  We study the long-time behaviour of a class of piecewise-deterministic Markov
processes which are an extension of some recent works. These $d$-dimensional
processes, d>=1, can especially be used to model the motion of a bacterium in
presence of a chemo-attractant, with parameters depending both on the position
and the velocity of the bacterium. Using the method of Meyn and Tweedie, we
show that under some good assumptions on the parameters of the model, such a
process converges exponentially fast towards its invariant measure. We also
establish the existence of exponential moments of the invariant measure using
results on semi-regenerative processes. The one-dimensional case is studied
separately since complementary results can be obtained in that particular case.
