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)
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)
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.
We extend recent results  on the existence of global phase-locked states (GPLS) in the Kuramoto model on a complete graph to the case of a complete bipartite graph. In particular, we prove that, for the Kuramoto model on a complete bipartite graph, the value of the critical coupling coefficient can be determined by solving a system of two nonlinear… (More)
We consider the game theoretic model of competitive information diffusion recently introduced in . We show that for the case of 2 competing agents, there exists a Nash Equilibrium for this game on any tree. We also present an example to show that this is not necessarily true for 3 or more agents.
For vehicle platoons, the leader following control architecture is known to be capable of achieving string stability while maintaining tight formations. In this paper we study a variety of schemes where the leader state is available to the other members of the platoon. We show that in some cases it is possible to achieve string stability in the presence of… (More)
This study examined some of the predictions made by cognitive models of psychosis, specifically the potential contribution of appraisals and trauma to the development of "need for care." Two groups reporting psychotic-like experiences with and without a "need for care" were compared on types of experiences, appraisals of these experiences, distress, and… (More)
Mental health professionals' attitudes towards deaf people were examined in relation to their previous contact with deaf people and their knowledge of deafness. Data were gathered regarding different aspects of contact, including the number and type of relationships participants had had with deaf people. A cognitive-processing theory of attitude change… (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)