Linear Systems Analysis

This course covers modeling and analysis of various systems, including electrical, biological, optical, and mechanical. We initially examine the most prominent properties and families of systems alongside fundamental concepts in system modeling, simulation, analysis, and synthesis. You will learn about the nodal analysis method and general concepts for formulating equations of resistive and dynamic electrical circuits. In modeling of biological, optical, and mechanical systems, you will learn about the underlying physical laws and their use for describing such systems with linear or nonlinear differential equations. You will learn about analysis of linear systems in time and frequency domain, solving higher-order differential equations or state-space equations, and learn about the transfer function, convolution, Laplace transform, and block diagrams. The course addresses key concepts such as stability, controllability, and observability of systems along with strategies for linearizing nonlinear systems. Finally, we will also explore basic analysis of discrete-time systems and discretization of continuous-time systems. The lectures are extensively supported with numerous examples of modeling natural and artificial systems and their analysis by analytical and numerical tools of the Python programming language. 

The purpose of this course is to provide the students with the basic knowledge and tools of modern linear systems theory in several domains. The students will gain knowledge on modelling, time and frequency domain analysis, state space approach, stability, controllability, and observability and illustrative aapplications of systems theory in optics and biological systems. The students will also be introduced to the computational tools for linear systems theory available in Matlab and Python.

The lectures provide a theoretical background on particular subjects together with presentation of simple illustrative examples. Additional examples are presented and discussed in tutorials. Practical work is being carried out within laboratory exercises, where students prepare reports for each assignment.