Linear multipass processes: a two-dimensional interpretation

Boland, Frank; Owens, D.H.

doi:10.1049/ip-d.1980.0032

Cited by 26 publications

(10 citation statements)

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“…(Kaczorek 1985, Tzafestas 1986, Chaudhry and Bedi 1989, Blyumin and Faradzhev 1982. Also, the 2-D approach arises naturally in describing multipass processes and modelling multivariable networks and large scale interconnected systems (Boland andOwens 1980, Willsky 1978).…”

Section: Introductionmentioning

confidence: 99%

Minimal circuit and state space realization of three-term separable denominator 2-D filters

Manikopoulos¹,

Mentzelopoulou²,

Antoniou³

1991

International Journal of Electronics

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A simple method is presented for the minimal state space realization of two dimensional(2-D)filters, with a three-term separable denominator (3TSD)made up of two 1-0 and one 2-D terms. The matrix A and the vectors b and e' of the state space model are derived explicitly from the coefficients of the initial transfer function. The circuit implementation for the 2-D 3TSD filters is provided, as well. The number of delay elements employed represents a significant reduction compared to earlier non-minimal realizations.

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Section: Introductionmentioning

confidence: 99%

Minimal circuit and state space realization of three-term separable denominator 2-D filters

Manikopoulos¹,

Mentzelopoulou²,

Antoniou³

1991

International Journal of Electronics

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“…Recall also that the repetitive processes here can be interpreted in 2D Roesser or Fornasini-Marchesini state-space model terms where for stability analysis the route is via the matrix defined earlier in this section. Then it can be shown that stability along the pass of the repetitive processes considered here is equivalent to asymptotic stability of its 2D discrete linear systems interpretation (Boland and Owens 1980;Rogers et al 2007). This stability equivalence does not hold for any other sub-classes of repetitive processes.…”

Section: Notementioning

confidence: 99%

“…This raised the question of whether or not there is another useful definition of this property and led to so-called practical BIBO stability for nD linear systems-see, for example, Agathoklis and Bruton (1983); Xu et al (1994Xu et al ( , 1997. The stability equivalence (Boland and Owens 1980) means that the practical stability analysis can also be applied to discrete linear repetitive processes (obviously the same sub-class for which this equivalence holds).…”

mentioning

confidence: 99%

“…process outputs) of pass profiles and (in its strongest form) is termed stability along the pass. Also it is possible to write the dynamics of a large sub-class of discrete linear repetitive processes in Roesser (or Fornasini-Marchesini) state-space model form and it has been shown that stability along the pass of a given example is equivalent to asymptotic or BIBO stability of its model interpretation (Boland and Owens 1980).…”

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confidence: 99%

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Strong practical stability and stabilization of discrete linear repetitive processes

Dąbkowski

Gałkowski

Rogers

et al. 2009

Multidim Syst Sign Process

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This paper considers two-dimensional (2D) discrete linear systems recursive over the upper right quadrant described by well known state-space models. Included are discrete linear repetitive processes that evolve over subset of this quadrant. A stability theory exists for these processes based on a bounded-input bounded-output approach and there has also been work on the design of stabilizing control laws, elements of which have led to the assertion that this stability theory is too strong in many cases of applications interest. This paper develops so-called strong practical stability as an alternative in such cases. The analysis includes computationally efficient tests that lead directly to the design of stabilizing control laws, including the case when there is uncertainty associated with the process model. The results are illustrated by application to a linear model approximation of the dynamics of a metal rolling process.

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“…The computational difficulties can be simplified by applying the results of Huang (1972) where it is shown that the stability condition given by the above lemma is equivalent to checking the conditions involving one-variable polynomials only. Then, using the results of Boland and Owens (1980), we can formulate the necessary and sufficient condition for stability along the pass in the following form.…”

Section: Linear Repetitive Processes and Their Stabilitymentioning

confidence: 99%

Robust control with finite frequency specification for uncertain discrete linear repetitive processes

Paszke

Bachelier

2012

Multidim Syst Sign Process

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This paper is dedicated to the study of robust stability and controller synthesis for discrete linear repetitive processes with polytopic uncertainty. In the robust control domain, conditions based on parameter dependent Lyapunov functions are proposed in order to reduce the conservatism related to uncertainty problems. The solution is a class of Lyapunov functions that depends in a polytopic way on the uncertain parameters and that can be derived from linear matrix inequality conditions. Nevertheless, in many cases in practice, the frequency range of reference signals, noises and disturbances are known beforehand. Therefore, performing controller synthesis in the full frequency range is not practically suited and may introduce conservatism to some extent. Based on generalized Kalman-YakubovichPopov Lemma, a finite frequency controller is derived for uncertain discrete linear repetitive processes which are the most investigated class of 2D systems. Hence, the designer can specify a frequency range where the prescribed control performance is required, where, for example, this range could be determined by inspection of frequency spectrums of the available signals.

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Linear multipass processes: a two-dimensional interpretation

Cited by 26 publications

References 0 publications

Minimal circuit and state space realization of three-term separable denominator 2-D filters

Minimal circuit and state space realization of three-term separable denominator 2-D filters

Strong practical stability and stabilization of discrete linear repetitive processes

Robust control with finite frequency specification for uncertain discrete linear repetitive processes

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