Realization of discrete-time nonlinear input–output equations: Polynomial approach

The aim of this paper is to solve reduction and realization problems for discrete-time multi-input multi-output nonlinear control systems by applying the theory of non-commutative polynomials. First, the necessary and sufficient reducibility condition is presented in terms of the greatest common lef...

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Bibliographic Details
Published in:Automatica (Oxford) 2012-02, Vol.48 (2), p.255-262
Main Authors: KOTTA, Ülle, TONSO, Maris
Format: Article
Language:English
Subjects:
Applied sciences
Computation
Computer science
control theory
systems
Control system analysis
Control theory. Systems
Differentials
Discrete-time systems
Dynamical systems
Equivalence
Exact sciences and technology
Input–output models
Mathematical analysis
Modelling and identification
Nonlinear control systems
Nonlinearity
Polynomial methods
Reduction
Representations
State space realization
System theory
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Summary:The aim of this paper is to solve reduction and realization problems for discrete-time multi-input multi-output nonlinear control systems by applying the theory of non-commutative polynomials. First, the necessary and sufficient reducibility condition is presented in terms of the greatest common left divisor of two polynomial matrices associated with the set of the higher order input–output (i/o) difference equations of the system. The condition also provides a method for system reduction, i.e. for finding the irreducible representation of the set of the i/o equations, being transfer equivalent to the original system representation. Second, to solve the realization problem, a formula is presented for computing the differentials of the state coordinates directly from the polynomial description of the nonlinear system. The polynomial approach addressed in this paper is more direct and requires noticeably less computations than earlier methods represented in terms of subspaces of differential one-forms.
ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2011.07.010