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mode state estimator. For example, a bound-  boundary scan test  a technique for
                              ary layer version of the discontinuous con-  applying scan design concepts to con-
                              troller                                trol/observe values of signal pins of IC com-
                                                                     ponents by providing a dedicated boundary-
                                u =−Us(e)/|s(e)|=−Usign(s(e)),
                                                                     scan register cell for each signal I/O pin.
                              where e is the control error and s is a function
                                                                     boundary value problem   a mathemat-
                              of e, may have the form
                                                                     ical problem in which the unknown is a so-

                                       −Usign(s(e)) if |s(e)| >ν     lution to a partial differential equation and is
                                 u =
                                        −Us(e)/ν  if |s(e)|≤ ν,      subject to a set of boundary conditions on the
                                                                     problem domain.
                              where ν> 0 is called the boundary layer
                              width.
                                                                     boundary values of 2-D general model
                                                                     let x i,j be a solution (semistate vector) to the
                              boundary layer controller  See boundary
                                                                     2-D generalized model
                              layer.
                                                                        x i+1,j+1 = A 0 x i,j + A 1 x i+1,j
                              boundary layer observer  See boundary
                              layer state estimator.                              + A 2 x i,j+1 + B 0 u i,j
                                                                                  + B 1 u i+1,j + B 2 u i,j+1
                              boundary layer state estimator  a con-
                              tinuous version of a sliding mode type state  i, j ∈ Z + (the set of nonnegative integers)
                                                                                 m
                              estimator, that is, a sliding mode type state  where u i,j ∈ R is the input and A k , B k (k =
                              estimator in which the right-hand side of the  0, 1, 2) are real matrices of the model. The
                                                                                  n
                              differential equation describing the estima-  vectors x i,j ∈ R whose indices lie on the
                              tor is continuous due to the introduction of a  boundary of the rectangle [0,N 1 ] × [0,N 2 ],
                              boundary layer to smooth out the discontin-  i.e., x i,0 ,  x i,N 2  for 1 ≤ i ≤ N 1 and
                              uous part of the estimator’s dynamics.  x 0,j ,x N 1 ,j for 0 ≤ j ≤ N 2 , are called
                                                                     boundary values of the solution x i,j to the 2-
                              boundary scan   a technique for applying  D general model. The boundary values may
                              scan design concepts to control/observe val-  be also given in other ways.
                              ues of the signal pins of IC components by
                              providing a dedicated boundary-scan register  boundary-element method (BEM)  a nu-
                              cell for each signal I/O pin.          merical method (integral equation technique)
                                                                     well suited to problems involving structures
                              boundary scan interface  a serial clocked  in which the dielectric constant does not vary
                              interface used to shift in test pattern or test  with space.
                              instruction and to shift out test responses in
                              the test mode. Boundary scan interface com-  bounded control  See saturating control.
                              prises shift-in, shift-out, clock, reset, and test
                              select mode signals.                   bounded distance decoding  decoding of
                                                                     an imperfect t-error correcting forward error
                              boundaryscanpath   atechniquethatuses  correction block code in which the corrected
                              a standard serial test interface to assure easy  error patterns are limited to those with t or
                              access to chip or board test facilities such as  fewer errors, even though it would be possi-
                              test registers (in an external or internal scan  ble to correct some patterns with more than t
                              paths) or local BIST. In particular it assures  errors.
                              complete controllability and observability of
                              all chip pins via shift in and shift out opera-  bounded function  a function x ∈ X e is
                              tions.                                 said to be bounded if it belongs also to the



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