ON D-STABILITY AND STRUCTURED SINGULAR-VALUES

It is shown in this paper that there are close connections between the notion of D-stability of a real square matrix and several quantities related to the structured singular value. As a main result, we show th at a real square matrix is D-stable if and only if the real structured singular value of some complex matrix is less than one. This conditio n implies that checking D-stability may in general be an NP-hard probl em. Since the exact verification of D-stability is difficult, we provi de several additional conditions that are either necessary or sufficie nt, and these conditions are also connected to the real or complex str uctured singular values. These results are further extended to the not ion of strong D-stability.