
Stability and stabilizability concepts for linear infinite dimensional dynamical systems
This lecture begins by describing in an introductory manner various concepts of stability of infinite dimensional systems with emphasis that, unlike in classical infinite dimensional linear systems, a variety of non equivalent stability types can be encountered in relatively simple PDEs systems. The
second part of this presentation is devoted to some by now classical tools to establish stability properties, namely in the frequency domain. Finally, a particular attention will be devoted to examples described by hyperbolic PDEs, where stabilization is achieved using collocated actuators and sensors.
The second part of this presentation is devoted to some by now classical tools to establish stability properties, namely in the frequency domain. Finally, a particular attention will be devoted to examples described by hyperbolic PDEs, where stabilization is achieved using collocated actuators and sensors. 
Backstepping methods
The use of linear Volterra operators in constructing backstepping transformations and feedback laws for stabilization of PDE systems by boundary control will be reviewed. Basic PDEs of both parabolic and hyperbolic types will be covered. With time permitting, an example of backstepping in observer design with boundary sensing will be covered.

From finite to infinite dimensional systems: approximation and interconnection issues
In practical problems the control laws of infinite dimensional systems are computed using projections on finite dimensional systems. Moreover, some applications are naturally described by couplings of infinite dimensional systems with finite dimensional ones. This presentation to describe the interconnections of these systems and the properties of the control laws computed on projected systems when inserted in the original infinite dimensional ones.
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