BIBO stability criteria for a certain class of discrete nonlinear systems

Kotsios, Stelios; Kalouptsidis, N.

doi:10.1080/00207179308923024

Cited by 22 publications

(12 citation statements)

References 5 publications

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“…Actually, we introduce the δǫ-operator which acts instead of to a single sequence to a pair of sequences. This initially appeared in [10] and has been examined in [18]. Let y(t), u(t) be two causal, real sequences, defined over the set of positive integers.…”

Section: The δǫ-Operators and The δǫ-Polynomialsmentioning

confidence: 99%

“…The following properties are valid for all the above operations. Their proofs are either obvious from the definitions and therefore omitted, or they can be found in [10], [18].…”

Section: The δǫ-Operators and The δǫ-Polynomialsmentioning

confidence: 99%

“…Specifically, we use the so-called δǫ-operator to deal with cross-products. This operator, introduced in [10], is an extension of the simple δ and ǫ-operators that are used in the algebraic description of nonlinear discrete input -output systems without cross-products [11], and which are also an extension of the simple shift operator q in linear discrete systems [21]. Via these operators we can define the so-called δ,ǫ and δǫ -polynomilas.…”

Section: Introductionmentioning

confidence: 99%

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The model matching problem for a class of polynomial non-linear discrete input–output systems with cross-products. An algorithmic approach

Kotsios

2009

International Journal of Control

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In this paper we examine the model matching problem that concerns non-linear input-output discrete systems, containing products among delays of input and output signals, through a special factorisation. The algebraic framework of -operators and the star-product that we adopt describe these systems. Moreover, a certain procedure that resembles the Euclidean division allows us to discover the linear factors of those systems, with respect to the above mentioned operations. The entire approach is symbolically algorithmic and involves the use of suitable software.

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Section: The δǫ-Operators and The δǫ-Polynomialsmentioning

confidence: 99%

“…The following properties are valid for all the above operations. Their proofs are either obvious from the definitions and therefore omitted, or they can be found in [10], [18].…”

Section: The δǫ-Operators and The δǫ-Polynomialsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The model matching problem for a class of polynomial non-linear discrete input–output systems with cross-products. An algorithmic approach

Kotsios

2009

International Journal of Control

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“…Several existing stability-When the maturation rate of a B-cell clone increases in response to a match between the clone's antibody and analysing methods for NARX models are time consuming and thus improper for implementation during the an antigen, aYnity maturation occurs. Those mutant cells are bound more tightly and stimulated to divide identi cation procedure [51][52][53]. Luh and Wu [54] have proposed a modi ed identi cation procedure to include more rapidly.…”

Section: Hence the Data Set S Can Be Represented As S=[ X Y]mentioning

confidence: 99%

Non-linear system identification using an artificial immune system

Luh

Cheng

2001

Proceedings of the Institution of Mechanical Engineers, Part I:

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In this paper, a novel non-linear system identi cation methodology is developed employing the features of the arti cial immune system. A simpli ed incremental approach integrated with the maximum entropy principle and an instantaneous feedback mechanism is proposed to reorganize the system's parameters simultaneously. To verify and demonstrate the eVectiveness of the proposed algorithm, a simulation example on a two-link robot was studied. This algorithm can achieve robustness and eYciency in identifying complex non-linear systems. The simulation results show that the identi ed immune models are robust to noise and various uncertainties in the robot dynamics.

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“…For the single-input single-output ility of the model. Kotsios and Kalouptsidis [45,46 ] (SISO) case, the NARX model is given as follows:…”

Section: Introductionmentioning

confidence: 99%

Inversion control of non-linear systems with an inverse NARX model identified using genetic algorithms

Luh

2000

Proceedings of the Institution of Mechanical Engineers, Part I:

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The inverse dynamics approach has been widely utilized in the control problem of various practical non-linear systems in recent years. This paper demonstrates a feedforward-feedback controller scheme of a non-linear plant whose dynamics are unknown and uncertain. The feedforward controller, an inverse NARX model (non-linear autoregressive model with exogenous inputs), provides only coarse control, whereas the feedback controller is used to handle unmodelled dynamics and disturbance. The inverse NARX model is derived by inverting the forward NARX model identified using genetic algorithms. A parallel-type NARX model whose outputs of the identification model are fed back into the identification model is adopted in the identification procedure to include the stability examination numerically. Both experimental and simulation results demonstrate that the proposed controller provides very good performance in the problems of input estimation and output tracking.

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BIBO stability criteria for a certain class of discrete nonlinear systems

Cited by 22 publications

References 5 publications

The model matching problem for a class of polynomial non-linear discrete input–output systems with cross-products. An algorithmic approach

The model matching problem for a class of polynomial non-linear discrete input–output systems with cross-products. An algorithmic approach

Non-linear system identification using an artificial immune system

Inversion control of non-linear systems with an inverse NARX model identified using genetic algorithms

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