CMMSE: State-space realization of periodic input/output quaternionic
linear systems
Abstract
The investigation of linear periodic systems is a prominent subject of
research within the domain of linear systems theory. In this context,
the state-space realization of such systems is of particular
significance. In fact, after successfully treating the realization
problem for time-invariant systems, various researchers have directed
their attention toward investigating the case of linear periodic
systems. Meanwhile, in the late 1980s, Jan C. Willems proposed an
approach that broadened the range of systems studied, now referred to as
the behavioral approach. This approach views the behavior of a system as
its fundamental element, including all signals that adhere to the system
laws (also called system trajectories). More recently, the behavioral
framework has also been extended separately to periodic and quaternionic
behavioral systems. Our work consists of considering linear periodic
input/output quaternionic behavioral systems and using recent
developments in order to obtain quasi-minimal and uniform state-space
realizations.