Canonical conservative state/signal shift realizations of passive discrete time behaviors

Canonical Realizations of Linear Time-Varying Systems

In this article, general scalar linear time-varying systems are addressed. In particular, canonical realizations with integrators, multipliers and adders are presented. Essentially, it is shown that the well-known configurations for constant systems can be generalized to the time-varying context by replacing the conventional eigenvalues by the earlier introduced dynamic eigenvalues. However, it...

Discrete Time Crystals: Rigidity, Criticality, and Realizations.

Despite being forbidden in equilibrium, spontaneous breaking of time translation symmetry can occur in periodically driven, Floquet systems with discrete time-translation symmetry. The period of the resulting discrete time crystal is quantized to an integer multiple of the drive period, arising from a combination of collective synchronization and many body localization. Here, we consider a simp...

Passive linear discrete time-invariant systems

We begin by discussing linear discrete time-invariant i/s/o (input/state/output) systems that satisfy certain ‘energy’ inequalities. These inequalities involve a quadratic storage function in the state space induced by a positive self-adjoint operator H that may be unbounded and have an unbounded inverse, and also a quadratic supply rate in the combined i/o (input/output) space. The three most ...

Unitary Shift-Register Realizations of Sequential Machines

Shift Register Realizations of Asynchronous Sequential Machines