  The paper is dedicated to studying the problem of existence and uniqueness of
solutions as well as existence of and exponential convergence to invariant
measures for McKean-Vlasov stochastic differential equations with Markovian
switching. Since the coefficients are only locally Lipschitz, we need to
truncate them both in space and distribution variables simultaneously to get
the global existence of solutions under the Lyapunov condition. Furthermore, if
the Lyapunov condition is strengthened, we establish the exponential
convergence of solutions' distributions to the unique invariant measure in
Wasserstein quasi-distance and total variation distance, respectively. Finally,
we give two applications to illustrate our theoretical results.
