Improving stability margins in discrete-time LQG controllers

Some of the problems are discussed which are encountered in the design of discrete-time stochastic controllers for problems that may adequately be described by the Linear Quadratic Gaussian (LQG) assumptions; namely, the problems of obtaining acceptable relative stability, robustness, and disturbance rejection properties. A dynamic compensator is proposed to replace the optimal full state feedback regulator gains at steady state, provided that all states are measurable. The compensator increases the stability margins at the plant input, which may possibly be inadequate in practical applications. Though the optimal regulator has desirable properties the observer based controller as implemented with a Kalman filter, in a noisy environment, has inadequate stability margins. The proposed compensator is designed to match the return difference matrix at the plant input to that of the optimal regulator while maintaining the optimality of the state estimates as directed by the measurement noise characteristics

Parents\u27 perceptions on the quality of information given by professionals regarding their deaf children

Many deaf children have delayed language development that would greatly affect their future academic success (Marschark, Lang, & Albertini, 2002). Information given by professionals to parents could be a significant factor in overcoming this delay. To assess the quality of this information six parents of deaf children in the Rochester NY area, three deaf parents and three hearing parents were selected to participate in an interview and survey. After the data was examined, it was found that the majority of the parents in this study felt that the information they received from professionals concerning their child\u27s language development was adequate but could use further improvements. These parents posted suggestions on possible ways that might help make the experience of working with professionals easier. More widespread research needs to be done on this topic, and possibly a guideline for professionals on how to work with parents of deaf children could be developed. Hopefully, this would help parents make easier and better decisions, which could ensure a more successful future for the deaf child

Absence of Luttinger's Theorem due to Zeros in the Single-Particle Green Function

We show exactly with an SU(N) interacting model that even if the ambiguity associated with the placement of the chemical potential, $\mu$, for a T=0 gapped system is removed by using the unique value $\mu(T\rightarrow 0)$, Luttinger's sum rule is violated even if the ground-state degeneracy is lifted by an infinitesimal hopping. The failure stems from the non-existence of the Luttinger-Ward functional for a system in which the self-energy diverges. Since it is the existence of the Luttinger-Ward functional that is the basis for Luttinger's theorem which relates the charge density to sign changes of the single-particle Green function, no such theorem exists. Experimental data on the cuprates are presented which show a systematic deviation from the Luttinger count, implying a breakdown of the electron quasiparticle picture in strongly correlated electron matter.Comment: Published version with supplemental material rebutting the recent criticism that our theorem fails if the ground-state degeneracy is lifte