LINEAR MULTIVARIABLE SYSTEMS

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.