Algebraic structures in linear systems theory

Algebraic Theory of Linear Systems: A Survey

An introduction into the algebraic theory of several types of linear systems is given. In particular, linear ordinary and partial differential and difference equations are covered. Special emphasis is given to the formulation of formally wellposed initial value problem for treating solvability questions for general, i. e. also underand overdetermined, systems. A general framework for analysing ...

Algebraic Solving of Complex Interval Linear Systems by Limiting ‎Factors‎

In this work, we propose a simple method for obtaining the algebraic solution of a complex interval linear system where coefficient matrix is a complex matrix and the right-hand-side vector is a complex interval vector. We first use a complex interval version of the Doolittle decomposition method and then we restrict the Doolittle's solution, by complex limiting factors, to achieve a complex in...

Algebraic systems theory and computer algebraic methods for some classes of linear control systems

Algebraic systems theory has been greatly advanced in the last 15 years. One the one hand, this is due to the behavioral approach to systems and control theory, which was introduced by J. C. Willems [17] in the 1980s, and which has proven to be particularly fruitful for algebraic approaches, as it studies solution sets rather than the representing equations, and it does not divide the system va...

Algebraic Analysis Applied to the Theory of Linear Dynamical Systems

The expression ”Algebraic Analysis” was coined by Mikio Sato. It consists of using algebraic notions to solve analytic problem. The origin of Algebraic Analysis is Algebraic Geometry as was developed by Alexander Grothendieck and his school. Mimicking the introduction of Grothendieck’s EGA (changing only a few words) one obtains a good definition of the modern theory of linear systems, as devel...

Lectures on Algebraic System Theory: Linear Systems Over Rings