CMMSE: State-space realization of periodic input/output quaternionic linear systems

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.