The paper describes the problem of identification of a linear discrete-time system in l(1), from noisy impulse response data of the system. Many tuned algorithms using window functions are proposed in the literature f...
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The paper describes the problem of identification of a linear discrete-time system in l(1), from noisy impulse response data of the system. Many tuned algorithms using window functions are proposed in the literature for the problem of H-infinity identification. The study concerns the use of suitable window functions and tuned and untuned algorithms for the problem of identification in l(1). The properties of window functions suitable for l(1) identification are analysed and it is shown that the use of a parameterised exponential window function leads to a convergent worst-case error. The optimal value of the window parameter which results in the least worst-case model error is given in terms of the a priori assumptions on the system and the noise. The tuned algorithm using the optimal parameter is proved to be robustly convergent.
We present a minimal lattice realization of MIMO linear discrete-time systems which interpolate the desired Markov and covariance parameters. The minimal lattice realization is derived via a recursive construction alg...
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We present a minimal lattice realization of MIMO linear discrete-time systems which interpolate the desired Markov and covariance parameters. The minimal lattice realization is derived via a recursive construction algorithm based on the state space description and it parametrizes all the interpolants.
We present a recursive algorithm for constructing lineardiscrete-lime systems which interpolate the desired 1st- and 2nd-order information. The recursive algorithm constructs a new system and connects it to the previ...
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We present a recursive algorithm for constructing lineardiscrete-lime systems which interpolate the desired 1st- and 2nd-order information. The recursive algorithm constructs a new system and connects it to the previous system in the cascade form every time new information is added. These procedures yield a practical realization of all the interpolants.
The problem of the determination of stability conditions for a linear discrete-time system having the cone-preserving property is addressed. Indeed, necessary and/or sufficient conditions are proposed in geometrical f...
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The problem of the determination of stability conditions for a linear discrete-time system having the cone-preserving property is addressed. Indeed, necessary and/or sufficient conditions are proposed in geometrical form using cones in order to characterize the stability properties (i.e., asymptotic stability, stability, instability) of discrete-timelinearsystems described by x k+1 = -Ax k , where matrix A has the property of leaving positively invariant a proper cone. Such a characterization does not use the knowledge of the spectral radius of matrix A. Des conditions nécessaires et/ou suffisantes sont proposées sous forme géométrique utilisant des cônes dans le but de caractériser les propriétés de stabilité (i.e., stabilité asymptotique, stabilité, instabilité) d'un système discret x k+1 = Ax k pour lequel la matrice A a la propriété de laisser positivement invariant un cône propre. Une telle caractérisation ne requiert pas la connaissance du rayon spectral de la matrice A
The goal of this paper is to point out and improve some inaccuracies in the mathematical formulation of linear discrete-time systems. We suggest an exact definition which covers all linearsystems used in practice. We...
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The goal of this paper is to point out and improve some inaccuracies in the mathematical formulation of linear discrete-time systems. We suggest an exact definition which covers all linearsystems used in practice. We show that the proof of the fundamental theorem of stability from [1,2] is incomplete and we give a correct one. In der vorliegenden Arbeit werden einige Ungenauigkeiten der mathematischen Formulierung der Theorie der digitalen linearen systeme besprochen. Das Anliegen der Verfasser war, eine exakte Definition dieser systeme zu erarbeiten, die für alle in der Praxis angewandten lineare systeme gülting wäre. Darüber hinaus wird die Unvolsständigkeit des Beweises des Stabilitätsgrundsatzes [1,2] nachgewiesen und eine Korrekte Beweisführung gegeben. Cet article a pour but de présenter et de corriger des imprécisions dans la formulation mathématique des systèmes digitaux linéaires. Nous suggérons une définition exacte qui couvrent tous les systèmes linéaires utilisés dans la pratique. Nous démontrons que la preuve du théorème fondamental de la stabilité dans [1, 2] incomplète et nous donnons une preuve correcte.
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