Finite- and fixed-time observers for uncertain multiple-outputs linear systems with unknown inputs

In this paper a family of homogeneity-based observers is proposed to estimate the state of a class of multiple-outputs linear systems with some parametric uncertainties and unknown inputs. Such a family of observers possesses robustness, finite- and fixed-time convergence properties depending on the considered parametric uncertainties and unknown inputs. The structure of these observers is simple since requires neither additional observers, for an a priori stabilization, nor complex transformations, and allows us to straightforwardly apply the observers for the case of multiple-outputs. The proposed structure is based on relative degree sufficient conditions that imply the strong observability of the system. Some simulation results illustrate the performance of the proposed homogeneous observers.