On fixed-time parameter estimation under interval excitation

The problem of estimation in the linear regression model is studied under the hypothesis that the regressor may be excited on a limited initial interval of time only. Then the estimation solution is based on the framework of finite-time or fixed-time converging dynamical systems. Two estimation algorithms are proposed. The robustness is analyzed using the notion of short-time input-to-state stability property with the use of a Lyapunov function. The performance of the estimators is demonstrated in numerical experiments.