Minimum-Radius Criterion for a Zonotopic State Estimator based on Degrees of Freedom^*

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. To address these issues, we propose here 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, whose complexity order is derived. The effectiveness of our approach is illustrated over two numerical examples, with one of them involving an interval method here modified to descriptor systems.