Realization of time-delay systems

Kaldmäe, Arvo; Kotta, Ülle

doi:10.1016/j.automatica.2018.01.001

Cited by 6 publications

(9 citation statements)

References 13 publications

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“…Example 1. Consider the system described by the i/o equation y (2) = (y (1) − u [1])u [1] + u (1) [2].…”

Section: Examplesmentioning

confidence: 99%

“…Thus, q 0 = − 1 − u [1], 1 = u (1) [1] + (1) 1 + 1 (u[1] + 1 ) and a 1 (s, ) = s − 1 − u [1]. Also, 2 s − 2u [1] + y (1)…”

Section: Examplesmentioning

confidence: 99%

“…This output really yields a strongly observable system, since one is able to find explicitly x 1 and x 2 from the expressions of y and y (1) . Then the i/o equation of (39) becomes y (2) = y (1) [1] y [1] [y (1) + ay − (1 − b)u] − ay (1) + (1 − b)u (1) + ry [1](u − y (1) ).…”

Section: Examplementioning

confidence: 99%

“…The problem has been studied for delay-free systems 1 and for time-delay systems with constant commensurable delays. [2][3][4] In this article we look for realizations of nonlinear single-input single-output (SISO) retarded control systems in the feedforward form. The importance of the feedforward form comes from its triangular structure, which has been useful in designing stabilizing controllers (see Reference 5 for delay-free and References 6-8 for time-delay case).…”

Section: Introductionmentioning

confidence: 99%

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Realizations in feedforward forms of nonlinear input‐output equations with time‐delays

Kaldmäe

Kawano

Kotta

2020

Intl J Robust & Nonlinear

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The article studies possibilities to find realization of nonlinear retarded control system with constant commensurable delays, described by higher order input-output equation, in a set of first-order equations, which is in the so-called feedforward form. Necessary and sufficient conditions are found for solvability of the problem when the realization is assumed to be strongly observable, that is, when the states of the feedforward form can be represented as functions of system output, input, their time-derivatives and delays. Though the extension follows, in general, the polynomial approach of the delay-free case, it is nontrivial. For instance, polynomial division is not, in general, possible for polynomials, defined over ring. Three examples illustrate the results.

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“…Example 1. Consider the system described by the i/o equation y (2) = (y (1) − u [1])u [1] + u (1) [2].…”

Section: Examplesmentioning

confidence: 99%

“…Thus, q 0 = − 1 − u [1], 1 = u (1) [1] + (1) 1 + 1 (u[1] + 1 ) and a 1 (s, ) = s − 1 − u [1]. Also, 2 s − 2u [1] + y (1)…”

Section: Examplesmentioning

confidence: 99%

Section: Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Realizations in feedforward forms of nonlinear input‐output equations with time‐delays

Kaldmäe

Kawano

Kotta

2020

Intl J Robust & Nonlinear

Self Cite

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“…Minimality of realizations is worked out in Kotta et al (2018) to characterize the largest class of delay free nonlinear systems for which the realization problem is well posed. A necessary and sufficient condition for the existence of a strongly observable realization is given in Kaldmäe et al (2018) for input-output systems with delays of retarded type.…”

Section: Introductionmentioning

confidence: 99%

A nonlinear time-delay realization for gastroparesis in patients with diabetes

Califano¹,

Scharbarg

Magdelaine

et al. 2019

Annual Reviews in Control

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The realization problem is fundamental in control systems theory and is well understood for linear systems. The situation is quite different for nonlinear systems with or without time delays. New results are given herein either as an abstract characterization of the class of delay-free nonlinear systems which are known to admit a realization, or by characterizing the existence of a realization for a wider class of retarded type or neutral type time delay nonlinear systems. The problem is motivated by the very practical modelling and realization problem of diabetes with or without gastroparesis. Up to 4% to 12% patients with diabetes are affected by the so-called gastroparesis which delays the digestion process. Several concurrent state space mathematical models do exist for diabetes and require a re-evaluation based on physiologic facts. These are reviewed herein to derive a (minimal) realization.

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