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\begin{document}

\title{Minimum-Radius Criterion for a Zonotopic State Estimator based on
Degrees of Freedom~~~~}



\author[1]{Alesi Augusto de Paula}%
\author[1]{Guilherme Raffo}%
\author[1]{Bruno Teixeira}%
\affil[1]{Affiliation not available}%


\vspace{-1em}



  
  \date{June 15, 2024}


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\begin{abstract}
This paper proposes a new cost criterion to enhance the precision of a
zonotopic state estimator for discrete-time descriptor linear systems.
Originally, the algorithm solves a minimum-trace problem involving
zonotopes, whose evolution is given by an interval observer structure
containing extra design matrices, called degrees of freedom. Although
the minimization of trace yields explicit solutions, it does not
necessarily imply minimization of volume, and thereby, the precision of
the output zonotope cannot be improved effectively. The volume measure
for zonotopes is computationally expensive and, when used as cost
criterion, implies nonlinear optimization problems. Motivated by such
issues, we here propose a minimum-radius criterion where the smallest
box enclosing the output zonotope is minimized. The resulting
optimization problem is nonlinear, but its convexity is exploited to
yield an equivalent linear program. The effectiveness of our approach is
illustrated over two numerical examples.%
\end{abstract}%



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