Bl-homogeneous sliding-mode observers for SISO linear time-varying systems with unknown input

Abstract

In this article, a family of state observers with bl- homogeneous properties is proposed for a class of linear systems with time-varying coefficients, in presence of an unknown input and with an arbitrary relative degree. The proposed observers converge globally and at least asymptotically to the true states for systems that satisfy the structural property of strong observability. With an adequate selection of gains and parameters the convergence is global and theoretically exact, in finite time or even more, in fixed time.