Functional Interval Observer for Discrete-Time Switched Descriptor Systems

Abstract

This article investigates functional interval observer based estimation methods for discrete-time switched descriptor systems with disturbances. A functional observer is presented using the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> formalism, and then a zonotope-based approach is applied to estimate its boundaries with a reduction of observer design constraints. To avoid the wrapping effect brought by the order reduction operations in the zonotope approach, reachability analysis is combined with the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> technique to design a switched functional interval observer with a better performance. Moreover, the relationship between the existing method, zonotope approach, and reachability analysis method is discussed in detail. The aforementioned methods are applied to an example for comparisons and to show their performance.