Sliding Mode Observers for Set-valued Lur'e Systems with Uncertainties Beyond Observational Range
Abstract
In this paper, we introduce a new sliding mode observer for Lur'e set-valued dynamical
systems, particularly addressing challenges posed by uncertainties not within the standard range
of observation. Traditionally, most of Luenberger-like observers and sliding mode observer have
been designed only for uncertainties in the range of observation. Central to our approach is the
treatment of the uncertainty term which we decompose into two components: the fi rst part in
the observation subspace and the second part in its complemented subspace. We establish that
when the second part converges to zero, an exact sliding mode observer for the system can be
obtained. In scenarios where this convergence does not occur, our methodology allows for the
estimation of errors between the actual state and the observer state. This leads to a practical
interval estimation technique, valuable in situations where part of the uncertainty lies outside
the observable range. Finally, we show that our observer is also a T- observer as well as a strong
H^∞ observer.
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