International audienc

This paper deals with the robust stabilization of a class of linear time varying systems. Instead of using a state observer or having dynamic structure, the controller is based on output derivative estimation. This allows the stabilization of linear time varying systems with very large parameter variation and a small number of controller parameters. The proof of stability is based on the polytopic representation of the closed loop and Lyapunov conditions. The result is proposed in a Linear Matrix Inequality (LMI) form. The validity of this approach is illustrated by a second order system case of study.

This work concerns the adaptation of sampling times for Linear Time Invariant (LTI) systems controlled by state feedback. Complementary to various works that guarantee stabilization independently of changes in the sampling rate, here we provide conditions to design stabilizing sequences of sampling instants. In order to reduce the number of these sampling instants, a dynamic scheduling algorithm optimizes, over a given sampling horizon, a sampling sequence depending on the system state value. Our proofs are inspired by switched system techniques combining Lyapunov functions and LMI optimization. To show the applicability of the technique, the theoretical study is illustrated by an implementation in Matlab/TRUE TIME.