The study of the stability properties of switched and hybrid systems gives rise to a number of interesting and challenging mathematical problems. The objective of this paper is to outline some of these problems, to review progress made in solving these problems in a number of diverse communities , and to review some problems that remain open. An important… (More)
We present a result on the existence of a common quadratic Lyapunov function for a pair of linear time-invariant systems. We show that this result charac-terises, generalises, and provides new perspectives on several well-known stability results. In particular, new time-domain formulations of the Circle Criterion and Meyer's extension of the KYP lemma are… (More)
It was recently conjectured that the Hurwitz stability of the convex hull of a set of Metzler matrices is a necessary and sufficient condition for the asymptotic stability of the associated switched linear system under arbitrary switching. In this paper we show that: (i) this conjecture is true for systems constructed from a pair of second order Metzler… (More)
BACKGROUND This study reports a new measure of psychotomimetic states in the context of cannabis and ketamine use. The Psychotomimetic States Inventory (PSI) has sub-scales of Delusory Thinking, Perceptual Distortions, Cognitive Disorganization, Anhedonia, Mania and Paranoia. METHODS The PSI was administered in two independent group, repeated measures… (More)
We present new necessary and sufficient conditions for the existence of fixed points in a finite system of coupled phase oscillators on a complete graph. We use these conditions to derive bounds on the critical coupling.
BACKGROUND Epidemiological evidence suggests a link between cannabis use and psychosis. A variety of factors have been proposed to mediate an individual's vulnerability to the harmful effects of the drug, one of which is their psychosis proneness. We hypothesized that highly psychosis-prone individuals would report more marked psychotic experiences under… (More)
The heterogeneity of schizotypal traits, suggested in previous research, was further investigated in a sample of subjects (N = 1095) administered a composite questionnaire consisting of a large number of published scales the majority of which were designed to measure psychotic characteristics. Factor analysis confirmed the four components previously… (More)
Psychotherapeutic interventions containing training in mindfulness meditation have been shown to help participants with a variety of somatic and psychological conditions. Mindfulness-based cognitive therapy (MBCT) is a meditation-based psychotherapeutic intervention designed to help reduce the risk of relapse of recurrent depression. There is encouraging… (More)
We consider the problem of common linear copositive function existence for positive switched linear systems. In particular, we present a necessary and sufficient condition for the existence of such a function for switched systems with two constituent linear time-invariant (LTI) systems. A number of applications of this result are also given.
In this paper we derive necessary and sufficient conditions for the existence of a common linear co-positive Lyapunov function for a finite set of linear positive systems. Both the state dependent and arbitrary switching cases are considered. Our results reveal an interesting characterisation of " linear " stability for the arbitrary switching case; namely,… (More)