A review of 2–D implicit systems
Automatica (Journal of IFAC)
Singular systems of partial difference equations
Multidimensional Systems and Signal Processing
Linear fractional representations of uncertain systems
Automatica (Journal of IFAC)
Stability Analysis for Linear Repetitive Processes
Stability Analysis for Linear Repetitive Processes
On the realization of 2-D linear systems with recursively computable latent variable models
IEEE Transactions on Circuits and Systems Part I: Regular Papers
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In modellingphysical systems it frequency turns out that only the so-calledsingular (also termed descriptor or implicit in the literature)form of the state equations can be obtained. Then the derivativeof the state vector for the continuous case or the next valueof the state vector for the discrete case is pre-multiplied bya square singular (or even rectangular) matrix. Such models havemore complex structure than their standard (also termed non-singularin the literature) counterparts with subsequent implicationsin terms of, for example, controller design. Note, however, thatsingularity is also useful, e.g. it can be used to derive theso-called semi-state description in cases when it is impossibleto derive the state space description. In some cases, however,singularity is not an intrinsic feature of the system but isdue, for example, to the effects of ’non-adequate‘ modellingor the method employed to construct the model. For a given exampleof this last case, a standard model may exist but is very difficultto construct. One way of avoiding singularity is to apply (ifpossible) well established algebraic transformations to the statevector. In this paper, an overview of recent results on singularityof equivalent state space realizations of 2D linear systems andmethods for avoiding this property is given. For example, therole of inversion and bilinear transformations in the latterrespect are treated together with singularity of the so-calledlinear repetitive processes and the introduction of this propertyas the result of discretization.