Instructor

Prof. John Lygeros

     

 

Course Intro

 

 

What should I know?

Linear algebra, ordinary differential equations, analysis of mechanical and electrical systems

What will I learn?

Mathematical modeling and classification of dynamic systems. 

Modeling of linear time-invariant systems with state space equations. Solution of state space equations in the time-domain and frequency domain. Stability, controllability and observability of dynamic systems. Description in the frequency domain; Bode plots and Nyquist diagrams. Sampled data and discrete-time systems. 

Advanced Topics: Nonlinear systems, Chaos, Discrete Event Systems, Hybrid Systems.

Syllabus

Modeling:

In this section students will learn to mathematically model and classify dynamic systems.

ODEs and linear algebra:

In this section students will recall theory on ordinary differential equations (ODEs) and linear algebra and will begin to apply these theories to models of dynamic systems.

Continuous time LTI systems in the time domain:

In this section students will learn to mathematically model dynamic systems as linear time invariant (LTI) systems using linear state space equations and provide a solution to the equations. They will learn to evaluate equilibria and stability of systems modeled using this form.

Energy, controllability, and observability:

Energy, controllability, and observability are introduced to the students for LTI systems in the time domain. They will learn conditions for controllability and observability and develop the skills necessary to build controllers and observers.

Continuous time LTI systems in the frequency domain:

In this section the students will learn to use analysis methods in the frequency domain to analyze the solution, stability, equilibria, controllability, and observability of continuous time LTI systems.

Discrete time LTI systems:

In this section the students will learn to model and analyze LTI dynamic systems modeled in discrete time. They will learn methods to evaluate the solution, equilibria, stability, controllability, and observability of discrete time LTI systems.

Nonlinear systems:

In this section the students will learn advanced topics associated with nonlinear systems. This includes understanding of multiple equilibria, advanced stability analysis and understanding of chaotic and switched systems