Section: New Results

Observality, controllability and stabilization in the time domain

In [27] , we dealt with the problem of the stabilization of a switched linear system, the feedback law being based on the optimization of a quadratic criterion. The Lyapunov function used for the design of this law defines a tight upper bound of the value of the cost for a quadratic optimization problem related to the system. Thus the obtained control law is sub-optimal.

In [19] we deal with the problem of the output stabilization of linear impulsive systems. These system are a mix of continuous and discrete-time system. An observer is synthesized and the stabilization is ensured through a feedback law which depends on the estimated state provided by the observer.

In [29] , we consider the design an high gain observers for a class of continuous dynamical systems with discrete-time measurements. In this work, the measurement sampling time is considered to be variable. Moreover, the new idea of the proposed work is to synthesize an observer requiring the less knowledge as possible from the output measurements. This is done by using an updated sampling time observer. Under the global Lipschitz assumption, the asymptotic convergence of the observation error is established. As an application of this approach, an state estimation problem of an academic bioprocess is studied, and its simulation results are discussed.

In [26] , we propose an MPC control scheme for a linear system with real-time constraints.

In [25] and [12] , we use precise energy estimates to provide an upper bound on the error made when replacing the dynamics of an infinite dimensional conservative quantum system by a finite dimensional projection.

In [34] , we give a set of sufficient conditions for approximate controllability of closed quantum systems when the dipolar approximation has to be replaced by a more realistic quadratic modeling.

In [35] , we investigate the regularity of propagators of bilinear control systems and extend a celebrated negative result of Ball, Marsden and Slemrod.

In [16] , we consider an infinite dimensional system modelling a boost converter connected to a load via a transmission line. The governing equations form a system coupling the telegraph partial differential equation with the ordinary differential equations modeling the converter. The coupling is given by the boundary conditions and the nonlinear controller we introduce. We design a nonlinear saturating control law using a Lyapunov function for the averaged model of the system. The main results give the well-posedness and stability properties of the obtained closed loop system.