Robustness of linear time-varying systems with relaxed excitation

International audienceIt is a well-known fact that linear time-varying systems with a persistently excited state matrix are exponentially converging and input-to-state stable with respect to additive perturbations. Recently, several relaxed conditions of persistent excitation have been presented [1], [2], which ensure an asymptotic convergence rate in the system. In the present work it is shown that these conditions are similar, and that under such a relaxed excitation only non-uniform in time input-to-state stability and integral input-to-state stability properties can be obtained. The results are illustrated by simulations for a problem of estimation in the linear regression model