Constructive Algebra for Systems Theory (CAST)

Algebraic methods have been successfully applied to problems arising in systems theory for a very long time now (see, e.g., [31, 65, 35, 30]). The most important reasons are the following. Algebra provides structural information about the systems under consideration, which could not be obtained by using numerical methods alone. An algebraic approach to linear control systems leads to a classification of structural properties of the system which can be characterized in algebraic terms and checked by symbolic computation, e.g. the fundamental notions of controllability, observability, and flatness. Using this algebraic language, multidimensional linear systems, also called n-dimensional systems, defined by partial differential equations, differential time-delay systems, discrete systems, repetitive systems, hybrid systems etc. can be treated simultaneously; depending on the type of the linear system under consideration one deals with modules defined over a (possibly non-commutative) polynomial ring which contains all functional operators that are present in the governing equations (e.g., differential/time-delay/shift operators). Therefore algebra provides a unified approach to system theoretic phenomena which are common to many types of multidimensional linear systems.