Linear Programming based Lower Bounds on Average Dwell-Time via Multiple Lyapunov Functions

With the objective of developing computational methods for stability analysis of switched systems, we consider the problem of finding the minimal lower bounds on average dwell-time that guarantee global asymptotic stability of the origin. Analytical results in the literature quantifying such lower bounds assume existence of multiple Lyapunov functions that satisfy some inequalities. For our purposes, we formulate an optimization problem that searches for the optimal value of the parameters in those inequalities and includes the computation of the associated Lyapunov functions. In its generality, the problem is nonconvex and difficult to solve numerically, so we fix some parameters which results in a linear program (LP). For linear vector fields described by Hurwitz matrices, we prove that such programs are feasible and the resulting solution provides a lower bound on the average dwell-time for exponential stability. Through some experiments, we compare our results with the bounds obtained from other methods in the literature and we report some improvements in the results obtained using our method.Comment: Accepted for publication in Proceedings of European Control Conference 202

On Stability of Measure Driven Differential Equations

International audienceWe consider the problem of stability in a class of differential equations which are driven by a differential measure associated with the inputs of locally bounded variation. After discussing some existing notions of solution for such systems, we derive conditions on the system's vector fields for asymptotic stability under a specific class of inputs. These conditions present a trade-off between the Lebesgue-integrable and the measure-driven components of the system. In case the system is not asymptotically stable, we derive weaker conditions such that the norm of the resulting trajectory is bounded by some function of the total variation of the input, which generalizes the notion of integral input-to-state stability in measure-driven systems

Input-to-State Stabilization in H1H^1-Norm for Boundary Controlled Linear Hyperbolic PDEs with Application to Quantized Control

International audienceWe consider a system of linear hyperbolic PDEs where the state at one of the boundary points is controlled using the measurements of another boundary point. For this system class, the problem of designing dynamic controllers for input-to-state stabilization in $H^1$-norm with respect to measurement errors is considered. The analysis is based on constructing a Lyapunov function for the closed-loop system which leads to controller synthesis and the conditions on system dynamics required for stability. As an application of this stability notion, the problem of quantized control for hyperbolic PDEs is considered where the measurements sent to the controller are communicated using a quantizer of finite length. The presence of quantizer yields practical stability only, and the ultimate bounds on the norm of the state trajectory are also derived

Evaluation of the effects of donepezil in psychotic disorders using Swiss albino mice

Background: Schizophrenia as a psychotic disorder is currently treated by various antipsychotic drugs. A large group of patients still remain resistant to the treatment and present in the form of residual cognitive deficits. Donepezil has been advocated at various conferences and seminars for using it in schizophrenia patients. Donepezil is currently approved drug for Alzheimer's disease to improve cognition. Hence, we have tried to assess its role for psychotic models induced by methylphenidate in mice.Methods: Methylphenidate 5 mg/kg was given by intraperitoneal (i.p) route to induce psychosis in Swiss albino mice (n=6). Donepezil was given alone in a dose of 1 mg/kg and in combination with low dose haloperidol 0.1 mg/kg and groups were compared with haloperidol 0.2 mg/kg. Activity of donepezil was also assessed on the haloperidol induced catalepsy test. Statistical analysis was done with ANOVA followed by Bonferroni’s test.Results: Methylphenidate successfully induced characteristic stereotypy behaviour in mice similar to amphetamine. Both donepezil 1 mg/kg and haloperidol 0.2 mg/kg showed significant reduction in stereotypy behaviour and there was no statistically significant difference between the two (p0.05).Conclusions: Methylphenidate can be used successfully to induce psychosis in animals and donepezil may be a promising and potentially useful drug as add on therapy to routine antipsychotics

Sub-Saharan African Immigrants’ Experiences in Utilizing Mental Health Services in Baltimore

AbstractMental illness is associated with poor quality of life evidenced by unemployment, homelessness, and substance abuse. Despite the adverse effects of mental illness, research has indicated that mental health-seeking behaviors and experiences in accessing mental health services among immigrants from sub-Saharan Africa are under-researched. The purpose of this qualitative study was to explore the experiences of sub-Saharan African immigrants in accessing mental health services in Baltimore, Maryland. To achieve the objective of this study, a descriptive research study was conducted utilizing semistructured one-on-one in-depth interviews with eight sub-Saharan African immigrants in Baltimore. Braun and Clarke’s six-step thematic data analysis approach was adopted resulting in five main findings. The study findings indicated the following: (a) stereotyped beliefs about mental health contributed to poor health-seeking behaviors among immigrants from sub-Saharan Africa, (b) there is limited mental health knowledge among sub-Saharan African immigrants, (c) low-income levels and lack of health insurance limit immigrants’ access to mental health services, (d) undocumented immigrants lack access to mental health services due to fear of deportation, and (e) low English language proficiency among immigrants limits access to mental health services. From the findings, it is plausible to conclude that sub-Saharan African immigrants face diverse challenges that hinder access to mental health services. The findings may bring about positive social change by improving the mental health outcomes and service utilization among sub-Saharan African immigrant populations