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Control Systems Seminars
Algebraic analysis of linear functional systems
INRIA, Saclay - Ile-de-France, France
Tuesday, 1 October 2013, at 11:00
Cybernetica Bldg (Akadeemia tee 21 1) ), room B 101
Abstract
The purpose of this talk is to show that a mathematical framework, called algebraic analysis, can be used to intrinsically study linear control systems and behaviours over Ore algebras. An Ore algebra is a non-commutative polynomial ring of functional operators which satisfy certain commutation rules. For instance, differential, time-delay, shift, divided difference? operators are elements of Ore algebras. Within this mathematical framework, we can study different classes of linear control systems such as time-varying ordinary differential systems, time-varying differential time-delay systems, partial differential systems or multidimensional discrete systems with constant or variable coefficients. The recent extension of Gröbner basis techniques to Ore algebras can be used to work effectively in these important classes of control systems. In this talk, we shall present algorithms which check whether or not a linear control systems over an Ore algebra is controllable, observable, parametrizable, flat, pi-free? Finally, we shall illustrate the main concepts, results and algorithms by explicit examples computed by the Maple package OreModules.