The course module aims at presenting the fundamental concepts for multivariable dynamic systems theory.
Course contents summary
1. Modeling, algebra and geometry in dynamical systems: Basic concepts of modeling - Introduction to Systems - Vector spaces and linear transformations - Matrix representation and projections - Summary of matrix algebra - Inner product - Orthogonality and orthogonal subspaces - Summary of algebra of subspaces - Eigenvectors and eigenvalues - Decomposition of Schur - Jordan canonical form - Invariant subspaces - Minimal polynomial.
2. Introduction to multivariable systems: The concept of state of a dynamical system – State transition matrix - Equivalent and indistinguishable states- Systems in minimal form – Equilibrium states - Motions and response of a system - Introduction to the concepts of reachability and controllability - Introduction to the concepts of observability and reconstructability.
Pdf slides of the lessons on the web site of the course.
G. Basile, G. Marro, "Controlled and conditioned invariants in linear system theory", Prentice-Hall, 1992
Classroom sessions with alternate use of slides and explanations at the blackboard. Discussion and resolution of exercises at the blackboard.