Internal Delay Research Articles

Delay-dependent Decentralized Stabilization of Multi-channel Singular Linear Continuous-time Systems with Multiple Point Delays

The delay-dependent decentralized stabilization problem of multi-channel singular time-delay time-invariant systems subject to multiple internal and external incommensurate constant point delays is discussed based on the descriptor integral-inequality approach. The descriptor integral-inequality Lemma is firstly established. Based on the new Lemma and the Lyapunov-Krasovskii functional approach, delay-dependent decentralized stabilization sufficient conditions are obtained. An LMI based algorithm to design the decentralized state feedback controls that stabilize the multi-channel singular time delays systems is provided. Finally, some numerical examples are presented to illustrate the effectiveness and the availability for the design.

About Robust Stability of Dynamic Systems with Time Delays through Fixed Point Theory

AbstractThis paper investigates the global asymptotic stability independent of the sizes of the delays of linear time-varying systems with internal point delays which possess a limiting equation via fixed point theory. The error equation between the solutions of the limiting equation and that of the current one is considered as a perturbation equation in the fixed- point and stability analyses. The existence of a unique fixed point which is later proved to be an asymptotically stable equilibrium point is investigated. The stability conditions are basically concerned with the matrix measure of the delay-free matrix of dynamics to be negative and to have a modulus larger than the contribution of the error dynamics with respect to the limiting one. Alternative conditions are obtained concerned with the matrix dynamics for zero delay to be negative and to have a modulus larger than an appropriate contributions of the error dynamics of the current dynamics with respect to the limiting one. Since global stability is guaranteed under some deviation of the current solution related to the limiting one, which is considered as nominal, the stability is robust against such errors for certain tolerance margins.

Ultrafast vibrational dynamics observed in higher electronic excited states of iodine using pump-UV DFWM spectroscopy

By using a combination of an initial pump pulse and a degenerate four-wave mixing process, we show that an interrogation of the vibrational dynamics occurring in different electronic states of molecules is possible. The technique is applied to iodine. The initial pump pulse is used to populate the B((3)Pi) state of molecular iodine in the gas phase. Now, by using an internal time delay in the DFWM process, which is resonant with the transition between the B state and a higher lying ion-pair state, the vibrational dynamics of the B state and the ion-pair state could be observed. States of even symmetry are investigated, which are accessed by a one photon transition from the B state. By a proper choice of the wavelengths used for the pump and DFWM beams, the dynamics of ion-pair states belonging to two different tiers are monitored.

Stabilization of the wave equation with boundary or internal distributed delay

We consider the wave equation in a bounded region with a smooth boundary with distributed delay on the boundary or into the domain. In both cases, under suitable assumptions, we prove the exponential stability of the solution. These results are obtained by introducing suitable energies and by proving some observability inequalities. For an internal distributed delay, we further show some instability results.

Stability Results for Switched Linear Systems with Constant Discrete Delays

This paper investigates the stability properties of switched systems possessing several parameterizations (or configurations) while being subject to internal constant point delays. Some of the stability results are formulated based on Gronwall′s lemma for global exponential stability, and they are either dependent on or independent of the delay size but they depend on the switching law through the requirement of a minimum residence time. Another set of results concerned with the weaker property of global asymptotic stability is also obtained as being independent of the switching law, but still either dependent on or independent of the delay size, since they are based on the existence of a common Krasovsky‐Lyapunov functional for all the above‐mentioned configurations. Extensions to a class of polytopic systems and to a class of regular time‐varying systems are also discussed.

UNKNOWN INPUTS OBSERVERS DESIGN FOR DELAY SYSTEMS

ABSTRACTThis paper concerns the design of functional, reduced and full order observers for linear time delay systems with unknown inputs. A new method generalizing those existing in the literature is presented for systems with unknown inputs, these unknown inputs are present in both the state and the measurement equations. Conditions for the existence of these observers are given and sufficient conditions for the stability independent of delays are derived using linear matrix‐inequality (LMI) formulation. The independent of internal delay and independent of delay cases are also presented. A numerical example is presented to illustrate our approach.

A Dynamic Stochastic Model for the Single Airport Ground Holding Problem

In this paper, we present a dynamic stochastic integer programming (IP) model for the single airport ground holding problem, in which ground delays assigned to flights can be revised during different decision stages, based on weather forecasts. The performance gain from our model is particularly significant in the following cases: (1) under stringent ground holding policy, (2) when an early ground delay program (GDP) cancellation is likely, and (3) for airports where the ratio between adverse and fair weather capacities is lower. The choice of ground delay cost component in the objective function strongly affects the allocation policy. When it is linear, the optimal solution involves releasing the long-haul flights at or near their scheduled departure times and using the short-haul flights to absorb delays if low-capacity scenarios eventuate. This policy resembles the current practice of exempting long-distance flights during ground delay programs. For certain convex ground delay cost functions, the spread of ground delay is more or less uniform across all categories of flights, which makes the overall delay assignment more equitable. Finally, we also present a methodology that could enable intra-airline flight substitutions by airlines after our model has been executed and scenario-specific slots have been assigned to all flights, and hence to the airlines that operate them. This makes our model applicable under the collaborative decision making (CDM) paradigm by allowing airlines to perform cancellations and substitutions and hence reoptimize their internal delay cost functions.

Practical criterion for delay estimation using random perturbations

Many systems contain an internal time delay, which significantly influences their dynamical properties. Methods to estimate this delay from times series in the presence of dynamical noise are not systematically studied. Addressing this problem, we demonstrate that it is sufficient to analyze the system's response to short-correlated external disturbances or internal noise. Following this idea, it is shown for linear and nonlinear systems, as well as for periodic dynamics, that the delay can be estimated by analyzing the correlation function. This method covers the case of strong noise and multiple delays.

Changing Dynamical Complexity with Time Delay in Coupled Fiber Laser Oscillators

We investigate the complexity of the dynamics of two mutually coupled systems with internal delays and vary the coupling delay over 4 orders of magnitude. Karhunen-Loève decomposition of spatiotemporal representations of fiber laser intensity data is performed to examine the eigenvalue spectrum and significant orthogonal modes. We compute the Shannon information from the eigenvalue spectra to quantify the dynamical complexity. A reduction in complexity occurs for short coupling delays while a logarithmic growth is observed as the coupling delay is increased.

Zero-Skew Driven Buffered RLC Clock Tree Construction

In nature an unbalanced clock tree exists in a SoC because the clock sinks of IPs have distinct input capacitive loads and internal delays. The construction of a bottom-up RLC clock tree with minimal clock delay and zero skew is crucial to ensure good SoC performance. This study proves that an RLC clock tree construction always has no zero skew owing to skew upward propagation. Specifically, this study proposes the insertion of two unit-size buffers associated with the binary search for a tapping point into each pair of subtrees to interrupt the non-zero skew upward propagation. This technique enables reliable construction of a buffered RLC clock tree with zero skew. The effectiveness of the proposed approach is demonstrated by assessing benchmarks.

On positivity of singular regular linear time-delay time-invariant systems subject to multiple internal and external incommensurate point delays

This paper deals with the positivity properties of singular regular linear time-delay time-invariant systems subject to multiple internal and external incommensurate constant point delays. The main idea behind the investigation is that its main body is performed based on the construction of the whole state-space trajectory solution without using as usual equivalence or similarity transformations on the matrix of dynamics in order to split the state-trajectory solution into two parts, one being typically associated with a nilpotent matrix. In that way, the whole state trajectory solution contains impulsive terms associated with the initial conditions and inputs. Some extensions concerning positivity aspects are given for a special canonical form which separates the dynamics associated with the nilpotent matrix obtained from an equivalence transformation on the singular matrix of the dynamic system.

Analysis of diffusion mechanism between gas and melt in gas-assisted injection molding

Abstract In the process of gas-assisted injection molding (GAIM), the high-pressure gas such as N 2 comes to a supercritical state. The supercritical N 2 diffuses into the polymer melt. After unloading the pressure, the N 2 in the polymer melt achieves a super-saturation state. The super-saturated N 2 close to the gas–melt interface diffuses through it, and the N 2 close to the internal wall delays to diffuse and remains in the polymer melt to form the small bubble, the inner pressure of small bubbles is bigger than outside pressure, so the small bubble has grown up gradually. Finally the cellular gas bubble blemish was formed. To decrease the gas bubble blemish, the gas holding pressure should be reduced in the precondition of the product quality is reached. And to eliminate the gas bubble blemish, the gas holding time should be increased as long as possible, and gas pressure should vent until molding part temperature comes down below its glassily temperature.

Excitable systems with internal and coupling delays

Two delayed coupled excitable systems with internal delays are studied. For different parametric values each of the isolated units displays excitable, bi-stable or oscillatory dynamics. Bifurcational relations among coupling time-lag and coupling constant for different values of the internal time-lags are obtained. Possible types of synchronization between the units in typical dynamical regimes are studied.

Quadratic stability and stabilization of switched dynamic systems with uncommensurate internal point delays

This paper deals with the quadratic stability and linear state-feedback and output-feedback stabilization of switched delayed linear dynamic systems with, in general, a finite number of non-commensurate constant internal point delays. The results are obtained based on Lyapunov’s stability analysis via appropriate Krasovsky–Lyapunov’s functionals and the related stability study is performed to obtain both delay independent and delay dependent results. It is proved that the stabilizing switching rule is arbitrary if all the switched subsystems are quadratically stable and that it exists a (in general, non-unique) stabilizing switching law when the system is polytopic, stable at some interior point of the polytope but with non-necessarily stable parameterizations at the vertices defining the subsystems. It is also proved that two subsystems individually parametrized in different polytopic-type sets which are not quadratically stable might be stabilized by a (in general, non-unique) switching law provided that a convexity-type condition is fulfilled at each existing pair of vertices, one corresponding to each subsystem. Some extensions are provided for a typical class of neutral time-delay systems.

Design of unknown input observer with H∞ performance for linear time-delay systems

A unknown input observer (UIO) design for a class of linear time-delay systems when the observer error can't completely decouple from unknown input is dealt with. A sufficient condition to its existence is presented based on Lyapunov stability method Design problem of the proposed observer is formulated in term of linear matrix inequalities. Two design problems of the observer with internal delay and without internal delay are formulated Based on H ∞ control theory in time-delay systems, the proposed observer is designed in term of linear matrix inequalities (LMI). A design algorithm is proposed The effective of the proposed approach is illustrated by a numerical example

Binaural and cochlear disparities

Binaural auditory neurons exhibit "best delays" (BDs): They are maximally activated at certain acoustic delays between sounds at the two ears and thereby signal spatial sound location. BDs arise from delays internal to the auditory system, but their source is controversial. According to the classic Jeffress model, they reflect pure time delays generated by differences in axonal length between the inputs from the two ears to binaural neurons. However, a relationship has been reported between BDs and the frequency to which binaural neurons are most sensitive (the characteristic frequency), and this relationship is not predicted by the Jeffress model. An alternative hypothesis proposes that binaural neurons derive their input from slightly different places along the two cochleas, which induces BDs by virtue of the slowness of the cochlear traveling wave. To test this hypothesis, we performed a coincidence analysis on spiketrains of pairs of auditory nerve fibers originating from different cochlear locations. In effect, this analysis mimics the processing of phase-locked inputs from each ear by binaural neurons. We find that auditory nerve fibers that innervate different cochlear sites show a maximum number of coincidences when they are delayed relative to each other, and that the optimum delays decrease with characteristic frequency as in binaural neurons. These findings suggest that cochlear disparities make an important contribution to the internal delays observed in binaural neurons.

Stimulus-locked responses of two phase oscillators coupled with delayed feedback

For a system of two phase oscillators coupled with delayed self-feedback we study the impact of pulsatile stimulation administered to both oscillators. This system models the dynamics of two coupled phase-locked loops (PLLs) with a finite internal delay within each loop. The delayed self-feedback leads to a rich variety of dynamical regimes, ranging from phase-locked and periodically modulated synchronized states to chaotic phase synchronization and desynchronization. Remarkably, for large coupling strength the two PLLs are completely desynchronized. We study stimulus-locked responses emerging in the different dynamical regimes. Simple phase resets may be followed by a response clustering, which is intimately connected with long poststimulus resynchronization. Intriguingly, a maximal perturbation (i.e., maximal response clustering and maximal resynchronization time) occurs, if the system gets trapped at a stable manifold of an unstable saddle fixed point due to appropriately calibrated stimulus. Also, single stimuli with suitable parameters can shift the system from a stable synchronized state to a stable desynchronized state or vice versa. Our result show that appropriately calibrated single pulse stimuli may cause pronounced transient and/or long-lasting changes of the oscillators' dynamics. Pulse stimulation may, hence, constitute an effective approach for the control of coupled oscillators, which might be relevant to both physical and medical applications.

Stability of Non-Neutral and Neutral Dynamic Switched Systems Subject to Internal Delays

This study deals with the quadratic stability and linear state-feedback and output-feedback stabilization of switched delayed linear dynamic systems with, in general, a finite number of non commensurate constant internal point delays. The results are obtained based on Lyapunov’s stability analysis via appropriate Krasovsky-Lyapunov’s functionals and the related stability study is performed to obtain both delay independent and delay dependent results. It is proved that the stabilizing switching rule is arbitrary if all the switched subsystems are quadratically stable and that it exists a (in general, non-unique) stabilizing switching law when the system is polytopic, stable at some interior point of the polytope but with non-necessarily stable parameterizations at the vertices defining the subsystems.

Properties of Absolute Stability in the Presence of Time Lags

This study is concerned with the properties of absolute stability independent of the delays of time-delay systems, possessing non commensurate internal point delays, for any nonlinearity satisfying a Popov’s- type time positivity inequality. That property holds if an associate delay-free system is absolutely stable and the size of the delayed dynamics is sufficiently small. The results are obtained for nonlinearities belonging to sectors [0, k] and [h, k+h], and are based on a parabola test type.

Absolute stability of feedback systems independent of internal point delays

The absolute stability, independent of the delays, of time-delay systems with non-commensurate internal point delays for any non-linearity satisfying a standard time positivity inequality is discussed. That property holds if an associate delay-free system is absolutely stable and the size of the delayed dynamics is sufficiently small. The results are obtained for non-linearities belonging to sectors [0, k] and [h, k+h], k≥0 and are based on a parabola test type.