1,977 research outputs found
An ISS Small-Gain Theorem for General Networks
We provide a generalized version of the nonlinear small-gain theorem for the
case of more than two coupled input-to-state stable (ISS) systems. For this
result the interconnection gains are described in a nonlinear gain matrix and
the small-gain condition requires bounds on the image of this gain matrix. The
condition may be interpreted as a nonlinear generalization of the requirement
that the spectral radius of the gain matrix is less than one. We give some
interpretations of the condition in special cases covering two subsystems,
linear gains, linear systems and an associated artificial dynamical system.Comment: 26 pages, 3 figures, submitted to Mathematics of Control, Signals,
and Systems (MCSS
Observability of Switched Linear Systems in Continuous Time
We study continuous-time switched linear systems with unobserved and exogeneous mode signals. We analyze the observability of the initial state and initial mode under arbitrary switching, and characterize both properties in both autonomous and non-autonomous cases
Global entrainment of transcriptional systems to periodic inputs
This paper addresses the problem of giving conditions for transcriptional
systems to be globally entrained to external periodic inputs. By using
contraction theory, a powerful tool from dynamical systems theory, it is shown
that certain systems driven by external periodic signals have the property that
all solutions converge to a fixed limit cycle. General results are proved, and
the properties are verified in the specific case of some models of
transcriptional systems. The basic mathematical results needed from contraction
theory are proved in the paper, making it self-contained
Avoidance Control on Time Scales
We consider dynamic systems on time scales under the control of two agents.
One of the agents desires to keep the state of the system out of a given set
regardless of the other agent's actions. Leitmann's avoidance conditions are
proved to be valid for dynamic systems evolving on an arbitrary time scale.Comment: Revised edition in JOTA format. To appear in J. Optim. Theory Appl.
145 (2010), no. 3. In Pres
A Characterization of Scale Invariant Responses in Enzymatic Networks
An ubiquitous property of biological sensory systems is adaptation: a step
increase in stimulus triggers an initial change in a biochemical or
physiological response, followed by a more gradual relaxation toward a basal,
pre-stimulus level. Adaptation helps maintain essential variables within
acceptable bounds and allows organisms to readjust themselves to an optimum and
non-saturating sensitivity range when faced with a prolonged change in their
environment. Recently, it was shown theoretically and experimentally that many
adapting systems, both at the organism and single-cell level, enjoy a
remarkable additional feature: scale invariance, meaning that the initial,
transient behavior remains (approximately) the same even when the background
signal level is scaled. In this work, we set out to investigate under what
conditions a broadly used model of biochemical enzymatic networks will exhibit
scale-invariant behavior. An exhaustive computational study led us to discover
a new property of surprising simplicity and generality, uniform linearizations
with fast output (ULFO), whose validity we show is both necessary and
sufficient for scale invariance of enzymatic networks. Based on this study, we
go on to develop a mathematical explanation of how ULFO results in scale
invariance. Our work provides a surprisingly consistent, simple, and general
framework for understanding this phenomenon, and results in concrete
experimental predictions
Unravelling social constructionism
Social constructionist research is an area of rapidly expanding influence that has brought together theorists from a range of different disciplines. At the same time, however, it has fuelled the development of a new set of divisions. There would appear to be an increasing uneasiness about the implications of a thoroughgoing constructionism, with some regarding it as both theoretically parasitic and politically paralysing. In this paper I review these debates and clarify some of the issues involved. My main argument is that social constructionism is not best understood as a unitary paradigm and that one very important difference is between what Edwards (1997) calls its ontological and epistemic forms. I argue that an appreciation of this distinction not only exhausts many of the disputes that currently divide the constructionist community, but also takes away from the apparent radicalism of much of this work
- …