Novel criteria for exponential stability of linear neutral time-varying differential systems

Using a novel approach, we get explicit criteria for exponential stability of linear neutral time-varying differential systems. A brief discussion to the obtained results is given. To the best of our knowledge, the results of this paper are new.

A reduced-order linear functional observer for linear stochastic systems

This paper presents necessary and sufficient conditions for the existence of a reduced-order linear functional state observer for linear stochastic systems. The order of the observer is the same as the dimension of the vectors to be estimated. A simple design algorithm is given together with a numerical example to illustrate the simplicity of the design procedure.

Observation-switching linear dynamic systems for tracking humans through unexpected partial occlusions by scene objects

This paper focuses on the problem of tracking people through occlusions by scene objects. Rather than relying on models of the scene to predict when occlusions will occur as other researchers have done, this paper proposes a linear dynamic system that switches between two alternatives of the position measurement in order to handle occlusions as they occur. The filter automatically switches between a foot-based measure of position (assuming z = Q) to a head-based position measure (given the person's height) when an occlusion of the person's lower body occurs. No knowledge of the scene or its occluding objects is used. Unlike similar research [2, 14], the approach does not assume a fixed height for people and so is able to track humans through occlusions even when they change height during the occlusion. The approach is evaluated on three furnished scenes containing tables, chairs, desks and partitions. Occlusions range from occlusions of legs, occlusions whilst being seated and near-total occlusions where only the person's head is visible. Results show that the approach provides a significant reduction in false-positive tracks in a multi-camera environment, and more than halves the number of lost tracks in single monocular camera views.

Partial state bounding with a pre-specified time of non-linear discrete systems with time-varying delays

In this study, the authors address a new problem of finding, with a pre-specified time, bounds of partial states of non-linear discrete systems with a time-varying delay. A novel computational method for deriving the smallest bounds is presented. The method is based on a new comparison principle, a new algorithm for finding the infimum of a fractal function, and linear programming. The effectiveness of our obtained results is illustrated through a numerical example.

An explicit criterion for finite-time stability of linear nonautonomous systems with delays

In this paper, the problem of finite-time stability of linear nonautonomous systems with time-varying delays is considered. Using a novel approach based on some techniques developed for linear positive systems, we derive new explicit conditions in terms of matrix inequalities ensuring that the state trajectories of the system do not exceed a certain threshold over a pre-specified finite time interval. These conditions are shown to be relaxed for the Lyapunov asymptotic stability. A numerical example is given to illustrate the effectiveness of the obtained result.

Constrained pole placement for linear systems using low-order output feedback controllers

The paper presents a simple approach to the problem of designing low-order output feedback controllers for linear continuous systems. The controller can place all of the closed-loop poles within a circle, C(- , 1/ β) , with centre at - and radius of 1/ β in the left half s-plane. The design method is based on transformation of the original system and then applying the bounded-real-lemma to the transformed system. It is shown that subjected to the solvability of an algebraic Riccati equation (ARE), output feedback controllers can then be systematically derived. Furthermore, the order of the controller is low and equals only the number of the open-loop poles lying outside the circle. A step-by-step design algorithm is given. Numerical examples are given to illustrate the design method.

Parameter-dependent H∞ control for time varying delay polytopic systems

This paper addresses the robust stabilization and H_∞ control problem for a class of linear polytopic systems with continuously distributed delays. The control objective is to design a robust H_∞ controller that satisfies some exponential stability constraints on the closed-loop poles. Using improved parameter-dependent Lyapunov Krasovskii functionals, new delay-dependent conditions for the robust H_∞ control are established in terms of linear matrix inequalities.

Applications of symbolic computing for symmetry analysis of differential equations

 This thesis presents a number of applications of symbolic computing to the study of differential equations. In particular, three packages have been produced for the computer algebra system MAPLE and used to find a variety of symmetries (and corresponding invariant solutions) for a range of differential systems.

Discrete inequalities based on multiple auxiliary functions and their applications to stability analysis of time-delay systems

Abstract
This paper presents new discrete inequalities for single summation and double summation. These inequalities are based on multiple auxiliary functions and include the Jensen discrete inequality and the discrete Wirtinger-based inequality as special cases. An application of these discrete inequalities to analyse stability of linear discrete systems with an interval time-varying delay is studied and a less conservative stability condition is obtained. Three numerical examples are given to show the effectiveness of the obtained stability condition.

Componentwise ultimate bounds for positive discrete time-delay systems perturbed by interval disturbances

This paper presents a method to derive componentwise ultimate upper bounds and componentwise ultimate lower bounds for linear positive systems with time-varying delays and bounded disturbances. The disturbance vector is assumed to vary within a known interval whose lower bound may be different from zero. We first derive a sufficient condition for the existence of componentwise ultimate bounds. This condition is given in terms of the spectral radius of the system matrices which is easy to check and allows us to compute directly both the smallest componentwise ultimate upper bound and the largest componentwise ultimate lower bound. Then, by using the comparison method, we extend the obtained result to a class of nonlinear time-delay systems which has linear positive bounds. Two numerical examples are given to illustrate the effectiveness of the obtained results.

Complexity theory and organizing form dualities

Purpose – The purpose of this paper is to describe how order-generated rules applied to organizing form dualities can assist in creating the conditions for emergent, self-organized behavior in organizations, thereby offering an operational deployment of complexity theory.

Design/methodology/approach – The paper begins by showing that the concept of dualities is consistent with complexity-thinking. In addition, when applied to organizing forms, dualities represent a practical way of affecting an organization's balance between chaos and order. Thus, when augmented with order-generating rules, organizing form dualities provide an access point for the practical instigation of edge of chaos conditions and the potential for emergence.

Findings – The paper maintains that many attempts to “manage” complexity have been associated with changes to organizing forms, specifically toward new forms of organizing. It is suggested that organizing form dualities provide some management guidance for encouraging the “edge of chaos” conditions advocated in complexity theory, although the details of self-organization cannot be prescribed given the assumptions of non-linearity associated with complexity theory perspectives. Finally, it is proposed that organizing dualities can elucidate the nature and application of order-generating rules in non-linear complex systems.

Practical implications – Dualities offer some guidance toward the practical implementation of complexity theory as they represent an accessible sub-system where the forces for order and chaos – traditional and new forms of organizing respectively – are accessible and subject to manipulation.

Originality/value – The commonalities between dualities and complexity theory are intuitive, but little conceptual work has shown how the former can be employed as a guide to managing organizing forms. Moreover, this approach demonstrates that managers may be able to stimulate “edge of chaos” conditions in a practical way, without making positivistic assumptions about the causality associated with their efforts.

The impact of column connection on band broadening in very high pressure liquid chromatography

A series of experiments was conducted to evaluate the degree of band broadening in very high pressure LC due to column connections. Different column manufacturers use slightly different designs for their column fittings. If the same column connections are repeatedly used to attach columns of different origins, different void volumes form between capillary tubes and column inlets. An Agilent Ultra Low Dispersion Kit (tubing id 75 μm) was installed on an Agilent Infinity 1290 ultra HPLC and used to connect successively an Agilent, a Phenomenex, and a Waters column. A series of uracil (unretained) samples were injected and eluted at a wide range of flow rates with a water/acetonitrile mixture as eluent. In order to determine the variance contribution from column connections as accurately as possible a nonretained probe compound was selected because the variance contribution from the column is the smallest for analytes, which have very low k values. Yet, this effect still has an impact on the resolution for moderately retained compounds (k > 2) for narrow-bore columns packed with fine particles, since variance contributions are additive for linear chromatographic systems. Each injection was replicated five times under the same experimental conditions. Then NanoViper column connections (tubing id 75 μm) were used and the same injections were made. This system was designed to minimize connection void volumes for any column. Band variances were calculated as the second central moment of elution peaks and used to assess the degree of band broadening due to the column connections. Band broadening may increase from 3.8 to 53.9% when conventional metal ferrules were used to join columns to connection sites. The results show that the variance contribution from improper connections can generate as much as 60.5% of the total variance observed. This demonstrates that column connections can play a larger role than the column packing with respect to band dispersion.

Discrete Wirtinger-based inequality and its application

In this paper, we derive a new inequality, which encompasses the discrete Jensen inequality. The new inequality is applied to analyze stability of linear discrete systems with an interval time-varying delay and a less conservative stability condition is obtained. Two numerical examples are given to show the effectiveness of the obtained stability condition.

An observer design procedure for a class of nonlinear time-delay systems

This paper considers a class of uncertain, nonlinear differential state delayed control systems and presents a reduced-order observer design procedure to asymptotically estimate any vector state functionals. The method proposed involves decomposition of the delayed portion of the system into two parts: a matched and mismatched part. Provided that the rank of the mismatched part is less than the number of the outputs, a reduced-order linear functional observer, with any prescribed stability margin, can be constructed by using a simple procedure. A numerical example is given to illustrate the new design procedure and its features.