Simultaneous stabilization of nD system via local-global principle

This paper addresses the relationship between the simultaneous stabilizability and the strong stabilizability of the multidimensional system. We present that the simultaneous stabilizability over a commutative ring cannot be given by the simultaneous stabilizability over its local rings in general. But if we have one-side coprime factorization, we show that solving the simultaneous stabilizability of the multidimensional system can be recast as solving the strong stabilizability of the multidimensional system. We consider the structural stability.