Nonlinear control systems: an introduction (2nd ed.)
Nonlinear control systems: an introduction (2nd ed.)
On global identifiability for arbitrary model parametrizations
Automatica (Journal of IFAC)
Representation for the radical of a finitely generated differential ideal
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
System identification (2nd ed.): theory for the user
System identification (2nd ed.): theory for the user
Modern computer algebra
Fast Algorithms for Manipulating Formal Power Series
Journal of the ACM (JACM)
Factorization-free decomposition algorithms in differential algebra
Journal of Symbolic Computation - Special issue on symbolic computation in algebra, analysis and geometry
A Gröbner free alternative for polynomial system solving
Journal of Complexity
Kronecker's and Newton's approaches to solving: a first comparison
Journal of Complexity
Convergence behavior of the Newton iteration for first order differential equations
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
Algebraic Complexity Theory
Geometric completion of differential systems using numeric-symbolic continuation
ACM SIGSAM Bulletin
A probabilistic algorithm to test local algebraic observability in polynomial time
Journal of Symbolic Computation - Computer algebra: Selected papers from ISSAC 2001
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Computing power series solutions of a nonlinear PDE system
ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
Notes on triangular sets and triangulation-decomposition algorithms II: differential systems
SNSC'01 Proceedings of the 2nd international conference on Symbolic and numerical scientific computation
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The following questions are often encountered in system and control theory. Given an algebraic model of a physical process, which variables can be, in theory, deduced from the input-output behavior of an experiment? How many of the remaining variables should we assume to be known in order to determine all the others? These questions are parts of the local algebraic observability problem which is concerned with the existence of a non trivial Lie subalgebra of the symmetries of the model letting the inputs and the outputs invariant.We present a probabilistic seminumerical algorithm that proposes a solution to this problem in polynomial time. A bound for the necessary number of arithmetic operations on the rational field is presented. This bound is polynomial in the complexity of evaluation of the model and in the number of variables. Furthermore, we show that the size of the integers involved in the computations is polynomial in the number of variables and in the degree of the system. Last, we estimate the probability of success of our algorithm.