抄録
This paper investigates some fundamental properties of nD systems whose input and output signals are unbounded in, at most, one dimension. Based on the nD Roesser state-space model, first of all, the concept of practical internal stability is introduced and a necessary and sufficient condition is derived. Solutions are also shown for the problems of practical-stabilization by local state feedback and construction of asymptotic state observer in the practical sense. Based on these results, the relationship between practical-BIBO stability and practical internal stability is clarified under the concepts of practical-detectability and practically-stabilizability. Finally, a connection between state-space and doubly coprime matrix fractional description on the ring of practically-stable rational functions is given.
The obtained results make it clear that all the above-mentioned control problems in the practical sense can be transformed to the corresponding 1D problems, therefore can be essentially solved by using 1D methods.
