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
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
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
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 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 use
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 (t
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 pre
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
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 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