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.