Dynamic output feedback finite-time control of LTI systems subject to parametric uncertainties and disturbances

In this paper we consider the output feedback, finite-time robust control problem for linear systems subject to time-varying parametric uncertainties and to unknown disturbances. The first result provided in the paper is a sufficient condition for finite-time staże feedback control in the presence of constant disturbances; such condition requires the solution of an Eigenvalue Problem,. Then we consider the more general output feedback case; sufficient conditions for robust finite-time control are given for different kind of controllers: static, dynamic, dynamic and gain scheduled with the parameters. The output feedback problems are shown to be reducible to the solution of optimization problems involving Bilinear Matrix Inequalities. Finally we deal with the case in which the disturbance is time-varying and generated by a linear system.