1,720,999 research outputs found
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
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
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
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
Stability and sensitivity analysis of an epidemiological model of genetic diseases
No full textThe epidemiology of X-linked recessive diseases, a class of genetic disorders, has been modeled through a discrete time, structured, mathematical system. The model accounts for both de novo mutations and distinct reproduction rates of procreating couples depending on their health conditions. Relying on Lyapunov’s and LaSalle method, asymptotic stabil- ity properties of model equilibrium points have been proved. Model’ sensitivity analysis has also been carried out to quantify the influence of model’s parameters on system’s response. The model allows to predict the spread over time in the population of any recessive genetic disorder transmitted through the X Chromosome
A multivariable stability margin in the presence of time-varying, bounded rate gains.
No full textIn this paper we consider a MIMO asymptotically stable linear plant. For such a system the classical con-
cepts of quadratic stability margin and multivariable gain margin can be dened. These margins have the
following interpretation: consider the closed-loop system composed of the plant and several real parameters,
one inserted in each channel of the loop; then any time-varying (time-invariant) parameters whose amplitudes
are smaller than the quadratic stability (multivariable gain) margin result in a stable closed-loop system. For
time-varying parameters whose magnitudes are between these two stability measures, stability may depend
on the rate of variation of the parameters. Therefore it makes sense to consider the stability margin given
by the maximal allowable rate of variation of the parameters which guarantees stability of the closed loop
system. As shown in this paper, a lower bound on this margin can be obtained with the aid of parameter
dependent Lyapunov functions
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