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Floquet prethermalization is observed in periodically driven quantum many-body systems where the system avoids heating and maintains a stable, non-equilibrium state, for extended periods. Here we introduce a novel quantum control method using off-resonance and short-angle excitation to significantly extend Floquet prethermal lifetimes. This is demonstrated on randomly positioned, dipolar-coupled, 13C nuclear spins in diamond, but the methodology is broadly applicable. We achieve a lifetime $T_2'~800 s at 100 K while tracking the transition to the prethermal state quasi-continuously. This corresponds to a >533,000-fold extension over the bare spin lifetime without prethermalization, and constitutes a new record both in terms of absolute lifetime as well as the total number of Floquet pulses applied (here exceeding 7 million). Using Laplace inversion, we develop a new form of noise spectroscopy that provides insights into the origin of the lifetime extension. Finally, we demonstrate applications of these extended lifetimes in long-time, reinitialization-free quantum sensing of time-varying magnetic fields continuously for ~10 minutes at room temperature. Our work facilitates new opportunities for stabilizing driven quantum systems through Floquet control, and opens novel applications for continuously interrogated, long-time responsive quantum sensors., Comment: 6 pages, 4 figures

Prethermal discrete time crystals (PDTCs) are a nonequilibrium state of matter characterized by long-range spatiotemporal order, and exhibiting a subharmonic response stabilized by many-body interactions under periodic driving. The inherent robustness of time crystalline order to perturbations in the drive protocol makes DTCs promising for applications in quantum technologies. We exploit the susceptibility of PDTC order to deviations in its order parameter to devise highly frequency-selective quantum sensors for time-varying (AC) magnetic fields in a system of strongly-driven, dipolar-coupled 13C nuclear spins in diamond. Integrating a time-varying AC field into the PDTC allows us to exponentially increase its lifetime, measuring improvement of up to three orders of magnitude (44,204 cycles), and results in a strong resonant response in the time crystalline order parameter. The linewidth of our sensor is limited by the PDTC lifetime alone, as strong interspin interactions help stabilize DTC order. The sensor operates in the 0.5-50 kHz range - a blind spot for sensors based on atomic vapor or electronic spins - and attains a competitive sensitivity. PDTC sensors are resilient to errors in the drive protocol and sample inhomogeneities, and are agnostic to the macroscopic details of the physical platform: the underlying physical principle applies equally to superconducting qubits, neutral atoms, and trapped ions., Comment: 7+16 pages

This paper studies the stabilization problem of networked control systems (NCSs) with random packet dropouts caused by stochastic channels. To describe the effects of stochastic channels on the information transmission, the transmission times are assumed to be deterministic, whereas the packet transmission is assumed to be random. We first propose a stochastic scheduling protocol to model random packet dropouts, and address the properties of the proposed stochastic scheduling protocol. The proposed scheduling protocol provides a unified modelling framework for a general class of random packet dropouts due to different stochastic channels. Next, the proposed scheduling protocol is embedded into the closed-loop system, which leads to a stochastic hybrid model for NCSs with random packet dropouts. Based on this stochastic hybrid model, we follow the emulation approach to establish sufficient conditions to guarantee uniform global asymptotical stability in probability. In particular, an upper bound on the maximally allowable transmission interval is derived explicitly for all stochastic protocols satisfying Lyapunov conditions that guarantee uniform global asymptotic stability in probability. Finally, two numerical examples are presented to demonstrate the derived results., Comment: 12 pages, 4 figures, accepted

Safety is essential for autonomous systems, in particular for interconnected systems in which the interactions among subsystems are involved. Motivated by the recent interest in cyber-physical and interconnected autonomous systems, we address the safe stabilization problem of interconnected systems with time delays. We propose multiple control Lyapunov and barrier functionals for the stabilization and safety control problems, respectively. In order to investigate the safe stabilization control problem, the proposed multiple control functionals are combined together via two methods: the optimization-based method and the sliding mode based method. The resulting controllers can be of either explicit or implicit forms, both of which ensure the safe stabilization objective of the whole system. The derived results are illustrated via a reach-avoid problem of multi-robot systems., Comment: 6 pages, 2 figures

This paper addresses the safe stabilization problem of stochastic nonlinear time-delay systems. Based on theKrasovskii approach, we first propose a stochastic control Lyapunov-Krasovskii functional to guarantee the stabilization objective and a stochastic control barrier-Krasovskii functional to ensure the safety objective. Both functionals are developed respectively for each control objectives for the first time. Since the optimization problem is not easy to be resolved for stochastic time-delay systems, we derive a sliding mode based approach to combine the proposed two functionals and to mediate stabilization and safety objectives, which allows to achieve the stabilization objective under the safety requirement. The proposed approach is illustrated via a numerical example., Comment: 7 pages, 8 figures. Accepted by IEEE TAC as a Technical Note. arXiv admin note: text overlap with arXiv:2204.12106