227-0225-00L Linear System Theory

Abstract	The class is intended to provide a comprehensive overview of the theory of linear dynamical systems, stability analysis, and their use in control and estimation. The focus is on the mathematics behind the physical properties of these systems and on understanding and constructing proofs of properties of linear control systems.
Objective	Students should be able to apply the fundamental results in linear system theory to analyze and control linear dynamical systems.
Content	- Proof techniques and practices. - Linear spaces, normed linear spaces and Hilbert spaces. - Ordinary differential equations, existence and uniqueness of solutions. - Continuous and discrete-time, time-varying linear systems. Time domain solutions. Time invariant systems treated as a special case. - Controllability and observability, duality. Time invariant systems treated as a special case. - Stability and stabilization, observers, state and output feedback, separation principle.
Lecture notes	Available on the course Moodle platform.
Prerequisites / Notice	Sufficient mathematical maturity with special focus on logic, linear algebra, analysis.