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This paper discusses stability and robustness properties of a recentlyproposed observer algorithm for linear time varying systems. The observer isbased on the approximation and subsequent modification of the non-negativeLyapunov exponents which yields a (non-uniform) exponentially stable errorsystem. Theoretical insights in the construction of the observer are given andthe error system is analyzed with respect to bounded unknown inputs. Therefor,new conditions for bounded input bounded state stability for linear timevarying systems are presented. It is shown that for a specific class of lineartime varying systems, a cascaded observer based on higher order sliding modedifferentiators can be designed to achieve finite time exact reconstruction ofthe system states despite the unknown input. A numerical simulation exampleshows the applicability of the proposed approach.

Non-Uniform Stability, Detectability, and, Sliding Mode Observer Design for Time Varying Systems with Unknown Inputs