Abstract: This paper studies theoretically some basic aspects of simultaneous stabilization of a finite set of plants. It is proved that four given plants are simultaneously stabilizable if and only if there exist four stable polynomials simultaneously satisfying two polynomial equations. If the obtained four polynomials satisfy only one of the polynomial equations, then there must exist two controllers having a common denominator or numerator such that each controller can simultaneously stabilize two of the four given plants. Further, the solvability of the polynomial equations is discussed and a design procedure of simultaneous stabilization of three plants is provided.

Key words: simultaneous stabilization, r obust cont rol, system design