Lecture 4 Notes: Continuous Topology Arguments
This lecture presents several techniques of qualitative systems analysis based on what is
frequently called topological arguments, i.e. on the arguments relying on continuity of
functions involved.
4.1
Analys
Lecture 6 Notes: Storage Functions And Stability Analysis
This lecture presents results describing the relation between existence of Lyapunov or
storage functions and stability of dynamical systems.
6.1
Stability of an equilibria
In this section we consid
Lecture 8 Notes: Local Behavior at Eqilibria
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 equilibrium.
8.1
First order conditions
This sec
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 stability of
periodic solutions.
9.1
Smooth Dependence o
Lecture 3 Notes: Continuous Dependence On Parameters
Arguments based on continuity of functions are common in dynamical system analysis.
They rarely apply to quantitative statements, instead being used mostly for proofs of
existence of certain objects (eq
Lecture 1 Notes: Input/Output and State-Space Models
This lecture presents some basic denitions and simple examples on nonlinear
dynam-ical systems modeling.
1.1
Behavioral Models.
The most general (though rarely the most convenient) way to dene a system
Lecture 2 Notes: Dierential Equations As System Models
Ordinary dierential requations (ODE) are the most frequently used tool for modeling
continuous-time nonlinear dynamical systems. This section presens results on existence
of solutions for ODE models,
Lecture 5 Notes: Lyapunov Functions and Storage
Functions
This lecture gives an introduction into system analysis using Lyapunov functions and
their generalizations.
5.1
Recognizing Lyapunov functions
There exists a number of slightly dierent ways of deni
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 continuous in the
usual sense.
10.1
Singularly perturbed OD
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 storage functions
The set of all real-valued functions