Reachability and observability indices of a discrete-time periodic descriptor system
Linear, finite-dimensional, discrete-time, descriptor control systems with periodic coefficients are considered. First, many concepts of reachability, observability and periodicity are introduced and discussed. Next, using the form of the solution of the difference state equation and purely algebraic methods, reachability and observability indices are analyzed and characterized. The connections between reachability and observability indices and certain linear subspaces in the state space are pointed out. Finally, using coprime decomposition of the nonproper transfer matrices, an algorithm for computing recurrently reachability and observability indices is proposed. Similar problems can be found in the paper [\textit{C. Coll}, \textit{M. J. Fullana} and \textit{E. Sánchez}, Appl. Math. Comput. 127, No. 2--3, 277--287 (2002; Zbl 1039.93039)].
Reachability and observability properties
scientific article; zbMATH DE number 2082066