caa a22 4500 477096956 CHVBK 20180405111530.0 cr unu---uuuuu 170330e19960101xx s 000 0 eng 10.1007/BF01187696 doi (NATIONALLICENCE)springer-10.1007/BF01187696 Bistritz Yuval Department of Electrical Engineering, Tel Aviv University, 69978, Tel Aviv, Israel aut Reflections on Schur-Cohn matrices and Jury-Marden tables and classification of related unit circle zero location criteria [Elektronische Daten] [Yuval Bistritz] We use the so-calledreflection coefficients (RCs) to examine, review, and classify the Schur-Cohn and Marden-Jury (SCMJ) class of tests for determining the zero location of a discrete-time system polynomial with respect to the unit circle. These parameters are taken as a platform to propose a partition of the SCMJ class into four useful types of schemes. The four types differ in the sequence of polynomials (the "table”) they associate with the tested polynomials by scaling factors: (A) a sequence of monic polynomials, (B) a sequence of least arithmetic operations, (C) a sequence that produces the principal minors of the Schur-Cohn matrix, and (D) a sequence that avoids division arithmetic. A direct derivation of a zero location rule in terms of the RCs is first provided and then used to track a proper zero location rule in terms of the leading coefficients of the polynomials of the B, C, and D scheme prototypes. We review many of the published stability tests in the SCMJ class and show that each can be sorted into one of these four types. This process is instrumental in extending some of the tests from stability conditions to zero location, from real to complex polynomial, in providing a proof of tests stated without a proof, or in correcting some inaccuracies. Another interesting outcome of the current approach is that a byproduct of developing a zero location rule for the Type C test is one more proof for the relation between the zero location of a polynomial and the inertia of its Schur-Cohn matrix. Birkhäuser, 1996 Circuits, Systems and Signal Processing Birkhäuser-Verlag 15/1(1996-01-01), 111-136 0278-081X 15:1<111 1996 15 34 https://doi.org/10.1007/BF01187696 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01187696 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Bistritz Yuval Department of Electrical Engineering, Tel Aviv University, 69978, Tel Aviv, Israel aut NATIONALLICENCE 773 0- Circuits, Systems and Signal Processing Birkhäuser-Verlag 15/1(1996-01-01), 111-136 0278-081X 15:1<111 1996 15 34 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer