Lecture 20 Notes: Local Stable Equilibrium
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 consider ODE models
x

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 equilibria
In this section we consider ODE models
x (t) = a

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 (though rarely the most convenient) way to dene a syste

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 relying on continuity of
functions involved.
4.1
Analysi

Lecture 3 Notes: Continuous Dependence
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 (equilibria, open

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 of slightly dierent ways of dening what constitutes a

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 existence of solutions for ODE models, which, in a syste

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

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 10 Notes: Singular Perturbations
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 ODE
In this sect

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
equilibrium.
8.1
First order conditions
This section describe