By Vladimír Strejc; International Federation of Automatic Control
Offers an invaluable reference resource on method constitution and regulate. Covers, linear structures, nonlinear platforms, strong keep an eye on, implicit method, chaotic platforms, singular and time-varying platforms.
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12) A(s), B(s) are 0- left coprime iff the 0-polynomial m atrices : A ( s ) , B (s) are 0-left coprime. ·1 1 ( s ) B 1 (s) = P1 (s), P2(s ) E P(p, m) in and 0-equivalence has the property of preserving the o structure i n n. ure in n of P1 (s), P�(s) may be can cclkd . Thus the pole structure in 0 is not i nvariant under n-equivalence. 3) The importance of n-equivalence is seen in Theorem 2. 0-cquivalence on P(p, m ) p r e ser ve s the zero struc ture in n. Example 1. Let 41 P1 (s) = ffi and P2 (s) = s + 1.
J. Co ntrol, 27, 657-672. , 199 1 : Linear Mullivaria b le Con t ro l, A lgebra ic A n a lysis a n d Synthesis Methods. Nelson-Wiley, London. (6] Verghese G . C . , 1979: Infin ite frequ ency beh a t,iou r ia gen eralized dynamical systems, P h. D. Thesis ,Stanford University, Stanford, CA. [7] Walker A . I3 . , 1988: Equivale n ce Tra nsfo rma tions for Lin e a r Systems, P h . D . Thesis, Hull University, Hull, England. oire d'Automatique d e Grenoble, URA CNRS 223 ENSIEG - INPG , BP 46 38402 St.
1 990). On Bezoutians of nonsquare matrix polynomials and inversion of matri ces with nonsquare blocks. Linear Algebra Appl . , 137- 1 3 8 , 249-323 . 0 0 From this Proposition and using the characterization of minimal periodic realizations by means of the block Hankel matrix associated to input-output periodic applications given by Sanchez, Hernandez and Bru ( 1 9 92,a), we establish the following result. Theorem 2. The rank of the periodic generalized Bezoutian matrix of (5) at time s is the dimension of the minimal periodic realizations of (5).