# NME130/Dynamical systems

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Dynamical systems in two parallel tracks

- Continuous time, time-invariant systems (6 hours)
- Differential equations and solutions
- Stabilizability
- Linearization
- Controllability and Observability
- Lyapunov equation/Lyapunov functions (show nonlinear case without proof)

- Finite state transition systems (6 hours)
- Finite automata
- Regular languages
- Linear temporal logic specifications

Discussion

- Why linear systems?
- May not be necessary
- Existence and uniqueness are harder in the nonlinear case
- Can probably start nonlinear, go linear by obs/ctr, then mention nonlinear again at the Lyapunov level

- Finite state machines
- Talk about LTL, Bucchi automata, etc

- How much should we focus on the tools
- Assume that people will do homework problems that make use of these
- Don't need to spend time in lecture going through the details
- No common tool set for many of these tools - could pose a problem

- Can we focus on similarities versus differences
- Take a point view of rings and fields, instead of focusing on the differences

Possible links to hybrid systems (3 more hours?)

- After presenting both topics, link to case study and/or generalizations
- Generalizations: numerical simulation, stability, etc
- Case study: hybrid models for UAVs, biological systems