Reachability, observability, and minimality for shift-invariant two-point boundary-value descriptor systems
In their nice paper the authors develop some of the system-theoretic properties of singular linear discrete-time two-point boundary value systems. They introduce two notions of shift-invariant systems, namely, displacement systems, for which the Green function is shift-invariant, and stationary systems, for which the input-output map is stationary. For such classes of systems the problem of reachability and observability is studied in detail. In particular, the authors give an effective criterion for weak reachability. In conclusion, the authors investigate the problem of minimality and extendibility. They underline that there is a certain degree of nonuniqueness in minimal realizations - both in the state space isomorphism and, more importantly, in the boundary and system matrices.
scientific article; zbMATH DE number 4141875
scientific article