Linearization of Discrete-Time Systems
SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization
An algebraic framework generalizing the concept of transfer functions to nonlinear systems
Automatica (Journal of IFAC)
Submersive rational difference systems and their accessibility
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Automatica (Journal of IFAC)
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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.