TY - JOUR
T1 - On D-stability and structured singular values
AU - Chen, Jie
AU - Fan, Michael K.H
AU - Yu, Cheng-Ching
PY - 1995/1/9
Y1 - 1995/1/9
N2 - 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 that 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 condition implies that checking D-stability may in general be an NP-hard problem. Since the exact verification of D-stability is difficult, we provide several additional conditions that are either necessary or sufficient, and these conditions are also connected to the real or complex structured singular values. These results are further extended to the notion of strong D-stability. © 1995.
AB - 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 that 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 condition implies that checking D-stability may in general be an NP-hard problem. Since the exact verification of D-stability is difficult, we provide several additional conditions that are either necessary or sufficient, and these conditions are also connected to the real or complex structured singular values. These results are further extended to the notion of strong D-stability. © 1995.
KW - D-stability
KW - Strong D-stability
KW - Structured singular values
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U2 - 10.1016/0167-6911(94)00036-U
DO - 10.1016/0167-6911(94)00036-U
M3 - 21_Publication in refereed journal
VL - 24
SP - 19
EP - 24
JO - Systems and Control Letters
JF - Systems and Control Letters
SN - 0167-6911
IS - 1
ER -