ON DISCRETE-TIME DIAGONAL AND D-STABILITY

This paper introduces four discrete-time analogs of different types of matrix stability: diagonal, simultaneous, vertex, and D-stability, th e last three being defined in terms of a certain (associated) polytope of matrices. The diagonal stability of any vertex of this polytope is shown to imply its simultaneous stability and hence D-stability of th e vertices. It is shown, by a counterexample, that D-stability, as in the continuous-time case, is not equivalent to diagonal stability. Sev eral important classes for which this equivalence is true are identifi ed. It is shown that simultaneous stability of the vertices is equival ent to the simultaneous stability of the whole polytope, and it is con jectured that this equivalence holds without the requirement of simult aneity. Some other conjectures relating the four types of stability ar e made, and it is shown that in the 2 X 2 case all four are equivalent .