117,802 research outputs found
On Output Feedback Control of Singularly Perturbed Systems
No full textWe treat the problem of robustness of output feedback controllers with respect to singular perturbations. Given a singularly perturbed control system whose boundary layer system is exponentially stable and whose reduced order system is exponentially stabilizable via a (possibly dynamical) output feedback controller, we present a sufficient condition which ensures that the system obtained by applying the same controller to the original full order singularly perturbed control system is exponentially stable for sufficiently small values of the perturbation parameter. This condition, which is less restrictive than those previously given in the literature, is shown to be always satisfied when the singular perturbation is due to the presence of fast actuators and/or sensors. Furthermore, we show explicitly that, in the linear time-invariant case, if this condition is not satisfied then there exists an output feedback controller which stabilizes the reduced order system but destabilizes the full order system
EQUILIBRIUM AND STABILITY ANALYSIS OF X-CHROMOSOME LINKED RECESSIVE DISEASES MODEL
No full textWe present a mathematical model describing the population distribution of genetic diseases related to X chromosomes. The model captures the disease spread within a population according to the relevant inheritance mechanisms; moreover it allows to include de novo mutations (i.e., affected siblings born to unaffected parents). The resulting dynamic system is nonlinear, discrete time and positive. Among our contributions, we consider the analytical study of model's equilibrium point, that is the distribution of the population among healthy, carrier and affected subjects, and the proof of the stability properties of the equilibrium point through Lyapunov second method. In particular global exponential stability was demonstrated in the presence of significant mutation rates and global asymptotic stability for negligible mutation rates
New converse Lyapunov theorems and related results on exponential stability (Article)
No full textWe treat the problem of constructing Lyapunov functions for systems which are, by assumption, exponentially stable. The construction we present results in a larger set of functions than those obtainable by previously known methods. A useful property of the proposed Lyapunov functions is that they preserve information on the rate of exponential convergence of the system. Some useful applications are given
Experimental investigation of vortex refrigeration
No full textThesis: B.S., Massachusetts Institute of Technology, Department of Mechanical Engineering, 1947Bibliography: leaf 19.by Robert J. Corless, Robert L. Solnick.B.S.B.S. Massachusetts Institute of Technology, Department of Mechanical Engineerin
Non Linear Discrete Time Epidemiological Model for X-Linked Recessive Diseases
No full textWe developed a discrete time, structured, mathe- matical model describing the epidemiology of X-linked recessive diseases, a class of genetic disorders.The model accounts for both de novo mutations and distinct reproduction rates of pro- creating couples depending on their health conditions. We found the exact solution to the model when de novo mutations are not significant and negligible reproduction rates are assigned to affected males. Our results have relevance for both system modeling and genetic epidemiology
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