@techreport{TR-IC-08-32,
  number = {TR-IC-08-32},
  author = {Nadir Matringe and Arnaldo Vieira-Moura and Rachid
                  Rebiha},
  title = {Morphisms for Non-trivial Non-Linear Invariant Generation
                  for Algebraic Hybrid Systems}, 
  month = {November},
  year = {2008}, 
  institution = {Institute of Computing, University of Campinas},
  note = {In English, 22 pages.
    \par\selectlanguage{english}\textbf{Abstract}
    We present a new method that addresses the various deficiencies of
    the state-of-the-art  non-linear invariant generation  methods for
    hybrid  systems.   Present  approaches  for  non-linear  invariant
    generation are  limited to  linear systems, or  they relay  on non
    scalable methods which have  high complexity. Moreover, for hybrid
    systems  with discrete transitions,  diferential rules,  and local
    conditions  that  are  described  by multivariate  polynomials  or
    fractional  systems,  no applicable  method  is  known that  lends
    itself  to  non-trivial   non-linear  invariants  generation.   We
    demonstrate a powerful computational complete method to solve this
    problem.    By  identifying   suitable   endomorphisms  for   each
    consecution condition,  we reduce the problem  to the intersection
    between  specific  eigenspaces  and initial  semi-affine/algebraic
    constraints.    Our   approach   avoids   first-order   quantifier
    elimination, Gröbner bases computation or direct resolution of the
    systems,  hereby circumventing  difficulties met  by  other recent
    techniques.
  }
}