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The design of practically stable \(nD\) feedback systems. (English) Zbl 0823.93033

In many practical situations of \(nD\) signal processing and systems, such as seismic and image processing, repetitive processes, there are several independent variables of an \(nD\) signal that are usually bounded spatial variables, except that one is the unbounded temporal variable. Agathoklis and Bruton developed the concept of practical BIBO stability for such a case and showed that the conventional BIBO stability is too restrictive for many applications.
The authors remined here this concept, solve the Bezout equation over the ring of practically stable rational functions and solve the problem of practical stabilizability of \(nD\) systems by using output feedback. They present also some examples and concluding remarks.
There is, however, one point that should be discussed. The problem considered here can be treated as some generalization of repetitive- multipass processes. The authors, following Agathoklis and Bruton, claim here that the effect of the existence of bounded variables in the model decreases restrictiveness of the stability conditions but Rogers and Owens write in: E. Rogers and D. H. Owens, Stability analysis for linear repetitive processes, Lect. Notes Control Inf. Sci. 175 (1992; Zbl 0772.93072) that if we assume an unbounded variable for the model instead of a bounded one for the real system, then the stability of such a generalized model does not have to guarantee the stability of the real system.

MSC:

93C35 Multivariable systems, multidimensional control systems
93D15 Stabilization of systems by feedback
93D25 Input-output approaches in control theory

Citations:

Zbl 0772.93072
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References:

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