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Stability and controllability of a class of 2-D linear systems with dynamic boundary conditions

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5 Author(s)
Rogers, E. ; Dept. of Electron. & Comput. Sci., Southampton Univ., UK ; Galkowski, K. ; Gramacki, A. ; Gramacki, J.
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Discrete linear repetitive processes are a distinct class of two-dimensional (2-D) linear systems with applications in areas ranging from long-wall coal cutting through to iterative learning control schemes. The feature which makes them distinct from other classes of 2-D linear systems is that information propagation in one of the two independent directions only occurs over a finite duration. This, in turn, means that a distinct systems theory must be developed for them. In this paper a complete characterization of stability and so-called pass controllability (and several resulting features), essential building blocks for a rigorous systems theory, under a general set of initial, or boundary, conditions is developed. Finally, some significant new results on the problem of stabilization by choice of the pass state initial vector sequence are developed

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Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on  (Volume:49 ,  Issue: 2 )