Stuart Townley

The effect of small delays in the feedback loop on the stability of neutral systems

It is well-known that exponential stabilization of a neutral system with unstable difference operator is only possible by allowing for control laws containing derivative feedback. We show that closed-loop stability of a neutral system with unstable open-loop difference operator obtained by applying a derivative feedback scheme is extremely sensitive to arbitrarily small time delays in the feedback loop.

Robustness of linear systems

Abstract In this paper we consider linear systems which are stable and examine the robustness of this property. The perturbations are assumed to have unbounded structure and we determine the smallest perturbation which destroys stability. We begin with an abstract analysis of the problem, but in later sections specialize to three types of systems: those whose mild solutions are given in terms of 1. (a) strongly continuous semigroups, 2. (b) resolvent operators-integrodifferential systems, 3. (c) evolution operators-time varying systems. For B a Banach space, L2(t0, T; B) denotes the space of all square integrable functions defined on [t0, T] with values in B. For B1, B2 Banach spaces, [t0, T] denotes the space of strongly measurable functions f(·):[t0, T]→L(B1, B2) with ess sup ∥f(·)∥⩽∞.B−1(t0, ∞;L(B1, B2)) denotes the space of strongly measurable functions f(·): [t0, ∞) → L(B1, B2) with ∥f(t)∥ 0 and k(·) ϵ L1(t0, ∞).

A framework for studying transient dynamics of population projection matrix models

Empirical models are central to effective conservation and population management, and should be predictive of real-world dynamics. Available modelling methods are diverse, but analysis usually focuses on long-term dynamics that are unable to describe the complicated short-term time series that can arise even from simple models following ecological disturbances or perturbations. Recent interest in such transient dynamics has led to diverse methodologies for their quantification in density-independent, time-invariant population projection matrix (PPM) models, but the fragmented nature of this literature has stifled the widespread analysis of transients. We review the literature on transient analyses of linear PPM models and synthesise a coherent framework. We promote the use of standardised indices, and categorise indices according to their focus on either convergence times or transient population density, and on either transient bounds or case-specific transient dynamics. We use a large database of empirical PPM models to explore relationships between indices of transient dynamics. This analysis promotes the use of population inertia as a simple, versatile and informative predictor of transient population density, but criticises the utility of established indices of convergence times. Our findings should guide further development of analyses of transient population dynamics using PPMs or other empirical modelling techniques.

Existence, learning, and replication of periodic motions in recurrent neural networks

A class of recurrent neural networks is shown to possess a stable limit cycle. A gradient type algorithm is used to modify the parameters of the network so that it learns and replicates autonomously a time varying periodic signal. The results are applied to controlling the repetitive motion of a two-link robot manipulator.

Low-Gain Control of Uncertain Regular Linear Systems

It is well known that closing the loop around an exponentially stable, finite-dimensional, linear, time-invariant plant with square transfer-function matrix

From PDEs with Boundary Control to the Abstract State Equation with an Unbounded Input Operator: A Tutorial

\BG(s)

Dynamics on Networks of Cluster States for Globally Coupled Phase Oscillators

compensated by a controller of the form

Integral control of linear systems with actuator nonlinearities: lower bounds for the maximal regulating gain

(k/s)\Gamma_0

Robustness with Respect to Delays for Exponential Stability of Distributed Parameter Systems

, where

Integral Control of Infinite-Dimensional Linear Systems Subject to Input Saturation

k\in {\Bbb R}