Differential and automatic equations (AO 102)

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.