Dynamic systems are the mathematical notions that make it possible to
modeling phenomena evolving over time, these phenomena being able to
come from physics, mechanics, economics, biology, ecology, chemistry ...
A dynamic system consists of a phase space, the space of the possible states of the phenomenon appropriately parametric, provided with a law of evolution which
describes the temporal variation of the state of the system. In the frame chosen here, the one
of laws of determinists in continuous time, this law of evolution takes the form of a
differential equation.
The explicit or even approximate resolution of a differential equation is in
generally impossible, the numerical methods allowing only to calculate on
a finite time interval a solution corresponding to initial conditions
data. The theory therefore aims rather at a qualitative study of phenomena and
seeks in particular to understand the long-term evolution.
The course "Dynamic Systems: Stability and Control" has two objectives.
The first is to approach the general study of dynamical systems governed by
Ordinary differential equations. The focus is mainly on the notion of
stability, the importance of which, for many practical problems, is comparable
to that of effective knowledge of solutions.
The second objective is to present an introduction to the control of the systems
dynamic, that is, automatic. In particular, it involves studying, in the
framework of linear automatic, the essential notions of commandability,
observability and stabilization.