Duality in time-varying linear systems: A module theoretic approach
This paper endeavours to give a more satisfactory treatment to the question of systems duality for time-varying linear systems than the general procedure of transposing matrices and changing signs. The authors use the module theoretic approach introduced by \textit{M. Fliess} [Syst. Control Lett. 15, No. 5, 391-396 (1990; Zbl 0727.93024)], where a left module represents the system, to define the dual system as the corresponding right module. Using this definition, the duality between controllability and observability as well as between state feedback and output injection are subsequently established. The Brunovsky form, an important canonical form for linear systems under static state feedback, is shown to be a canonical form for controllable linear time-varying systems under quasistatic state feedback as well. The dual result is also given. It is shown that the classical observability indices can be introduced by using filtrations and the classical controllability indices may then be defined by duality. Two examples complete this paper.
scientific article; zbMATH DE number 931922
scientific article