Abstract
Given a couple of D stability domains in the coefficient space of interval polynomials, what kind of total information can we draw from them altogether? This motivates the present paper and we address ways of merging and extending given two D stable hyper-boxes in the coefficient space. We show that it is in general possible to enlarge a stability interval at the expense of reductions in the other intervals provided the two boxes share a non-empty part. Even when they have no intersections, for some specific D domains in the complex plane, we can merge two separate intervals into a single one, thus yielding anew stability region in the coefficient space. This can, however, be done only when two intervals along a single coefficient axis are disjoint and along the other axes not. This restriction can be eased for some D domains such as open left half complex plane, right and left half of real axis and imaginary axis. For these domains, two intervals in the odd-order term coefficient axes or even-order term coefficient ones are allowed to be separate. In all these results existence of the two D stability boxes areassumed a priori, for simplicity. We next propose easy methods to generate a new D stability box based on a given one. Successive use of these methods yields a series of new boxes in quite a simple manner. Combining this technique with the above merger method, extension of a D stability interval along a desired coefficient axis becomes possible. To illustrate the results presented, some simple numerical examples are worked out.
