Introduction to Systems Theory
EduOpen online course
This course is aimed at anyone who wants to learn the basics of systems theory and who has a university background in mathematical analysis (including Laplace transform), linear algebra, and physics.
State models with one input and one output will be covered, highlighting their importance and main properties; it will also be shown how to construct such models from the equations of physics.
The topics covered in the course are:
- Definitions of state models, linear systems, construction of a state model, choice of state variables, equilibrium points and linearization, feedback linearization.
- Analysis of linear systems: evolution of state and output of a linear system, “superposition of effects” principle, free and forced evolution of state and output, transfer function and impulse response.
- Stability: stability in linear systems, stability conditions for equilibrium points of non-linear systems, BIBO stability. Examples: compartmental models, predator-prey model (Lotka-Volterra), electric motor model