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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Vydané v:Automatica (Oxford) Ročník 48; číslo 2; s. 255 - 262
Hlavní autori: KOTTA, Ülle, TONSO, Maris
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Kidlington Elsevier Ltd 01.02.2012
Elsevier
Predmet:
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
Discrete-time systems
Polynomial methods
Nonlinear control systems
Reduction
Input–output models
State space realization
MIMO system
Polynomial matrix
Reducibility
System realization
Necessary and sufficient condition
Differential form
Non linear control
Polynomial equation
Systems theory
Polynomial method
Input-output models
Difference equation
Non linear system
Irreducible representation
Discrete time
System representation
Input output model
ISSN:0005-1098, 1873-2836
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Popis
Shrnutí: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.
Bibliografia:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2011.07.010