A stabilization criterion for matrix pencils under bilinear transformation

In the literature, the dual matrix pencils sF - G and F - over(s, ̂) G are identified with the homogeneous pencil sF - over(s, ̂) G. In the present paper, for a given a homogeneous pencil which is unstable, in the sense that it has roots in the closed right half-plane, a bilinear transformation is determined such that the new homogeneous bilinear-equivalent matrix pencil is stable. The notion of bilinear equivalence is introduced and a stabilization criterion of a homogeneous matrix pencil is finally derived.