Colloquium Mathematics - Sutrisno, University of Groningen

Title: Singular Switched Systems in Discrete Time: Solvability, Observability, and Reachability Notions

Abstract:

Discrete-time singular (switched) systems, also known as (switched) difference-algebraic equations, have in general three solvability issues: inconsistent initial values, nonexistence or nonuniqueness of solutions, and noncausalities, which are generally not desired in applications. To deal with those issues, new solvability notions are proposed in the study, and the corresponding necessary and sufficient conditions have been derived with the help of (strictly) index-1 notions. Furthermore, surrogate (switched) systems--ordinary (switched) systems that have equivalent behavior--have also been established for solvable systems. By utilizing those surrogate systems, fundamental analysis including observability, reachability, and stability has also been characterized.