Lecture 1 Notes: Input/Output and State-Space Models
1
This lecture presents some basic denitions and simple examples on nonlinear
dynam-ical systems modeling.
1.1
Behavioral Models.
The most general
Lecture 7 Notes: Finding Lyapunov Functions
This lecture gives an introduction into basic methods for nding Lyapunov functions and
storage functions for given dynamical systems.
7.1
Convex search for
Lecture 6 Notes: Storage Functions
This lecture presents results describing the relation between existence of
Lyapunov or storage functions and stability of dynamical systems.
6.1
Stability of an equi
Lecture 5 Notes: Lyapunov Functions
This lecture gives an introduction into system analysis using Lyapunov
functions and their generalizations.
5.1
Recognizing Lyapunov functions
There exists a number
Lecture 4 Notes: Analysis Based On Continuity
This lecture presents several techniques of qualitative systems analysis based on
what is frequently called topological arguments, i.e. on the arguments r
Lecture 2 Notes: Dierential Equations
Ordinary dierential requations (ODE) are the most frequently used tool for
modeling continuous-time nonlinear dynamical systems. This section presens
results on e
Lecture 13 Notes: Feedback Linearization
Using control authority to transform nonlinear models into linear ones is one of
the most commonly used ideas of practical nonlinear control design. Generally,
Lecture 10 Notes: Singular Perturbations and Averaging
This lecture presents results which describe local behavior of parameter-dependent
ODE models in cases when dependence on a parameter is not cont
Lecture 9 Notes: Local Behavior Near Trajectories
This lecture presents results which describe local behavior of ODE models in a
neigbor-hood of a given trajectory, with main attention paid to local s
Lecture 8 Notes: Local Behavior
This lecture presents results which describe local behavior of autonomous systems
in terms of Taylor series expansions of system equations in a neigborhood of an
equili