Computation of the fundamental matrix sequence and the Cayley-Hamilton theorem in singular 2-D systems
The study of 2-D singular or generalized systems was the objective of a number of papers recently. The 2-D generalized state-space models may provide a more suitable structure for a number of applications, such as processing of images, and in heat flow exchangers, long trasmission lines, neural networks, multivariable networks and interconnected 2-D systems. Recently we have defined (with F.L. Lewis) the fundamental matrix of the 2-D generalized Roesser model and demonstrated a number of properties and its fundamental importance in the analysis of 2-D generalized systems. This paper refers to a computational technique for the calculation of the fundamental matrix sequence. Using a three dimension recursion algorithm, and exploing the Toeplitz and Hessenberg forms of certain auxiliary matrices, each matrix of the fundamental matrix sequence is expressed via an ARMA model. Moreover the generalized 2-D Caley-Hamilton theorem is presented, in terms of the fundamental matrix sequence. The presented algebraic results provide useful tools for the analysis and design of 2-D generalized state-space systems.
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