We address the problem of determining the minimum bit-rate needed to stabilize a linear time-invariant process. For the noise free case, we determine a bit-rate below which stabilization is not possible and above which asymptotic stabilization can be achieved. Inspired by differential pulse code modulation (DPCM) techniques, we propose practical encoding/decoding schemes that guarantee boundedn...

We prove that under rather general assumptions an exactly controllable problem is uniformly stabilizable with arbitrarily prescribed decay rates. Our approach is direct and constructive and avoids many of the technical difficulties associated with the usual methods based on Riccati equations. We give several applications for the wave equation and for Petrovsky systems.

Aggregation of sub-micron and nano-sized polystyrene latex particles was studied in room temperature ionic liquids (ILs) and in their water mixtures by time-resolved light scattering. The aggregation rates were found to vary with the IL-to-water molar ratio in a systematic way. At the water side, the aggregation rate is initially small, but increases rapidly with increasing IL content, and reac...

STUDY DESIGN  Comparative effectiveness review. STUDY RATIONALE  Spinal fusion is believed to accelerate the degeneration of the vertebral segment above or below the fusion site, a condition called adjacent segment disease (ASD). The premise of dynamic stabilization is that motion preservation allows for less loading on the discs and facet joints at the adjacent, non-fused segments. In theory...

There has recently been significant interest in feedback stabilization problems over communication channels, including several with bit rate limited feedback. Motivated by considering one source of such bit rate limits, we study the problem of stabilization over a signal-to-noise ratio (SNR) constrained channel. We discuss both continuous and discrete time cases, and show that for either state ...