Analysis and Synthesis of Realizable Non-equilibrium Dissipative Structures

Computation complexity of a broad variety of practical design problems is known to be strongly depending on an algebraic complexity of corresponding mathematical system representations. Especially some vector-matrix models are frequently used in numerous interdisciplinary fields. One way to overcome the complexity problems is based on some special algebraic structures of low order model approximations, such as e.g. balanced representations. Another approach based on the concept of sparse matrices has also become very popular. As a very successful special case of sparse matrix based approach a class of tridiagonal system representations [1] has found applications in solution of partial differential equations, digital signal processing, image processing, computational fluid dynamics, spline curve fitting and many others. In this contribution a generalized sparse matrix motivated multi-diagonal method is proposed and some new results, based on state space energy motivated causal system representations are presented, too [2]