In this paper, we give sufficient and necessary conditions for operator ma trix to generate an exponentially bounded semigroup, where A1 and A0 are the coefficent operators of the complete sedond order abstract Cauchy problem (ACP2). we also give the relationship between the fact that generates an exponentially bounded semigroup and the C-wellposedness of semigroup and the C-wellposedness of (ACP2). Finally, we apply these,esult and those in [3] to discuss the C-wellposedness of a kind of (ACP2) with application background.