Impulse Times Research Articles

An impulse-time perturbation approach for enhancing the robustness of extra-insensitive input shapers

In this paper, perturbation-based extra-insensitive input shapers (PEI-ISs) are proposed to enhance the robustness of the input shaping technique. The extra-insensitive input shaper (EI-IS) has been known to be more robust than the so-called derivative input shapers such as ZVD, ZVDD, and ZVDDD shapers. However, the robustness of the known EI-IS is restricted by the symmetric property in the sensitivity curve. To address this, the PEI-IS is devised by multiplying a series of input shapers in the Laplace domain, of which the impulse times are slightly perturbed from those of the zero vibration (ZV) shaper. For a single-hump case, a closed-form solution to the PEI-IS is provided. For two- and three-hump cases, the approximate solutions are presented. The robustness is evaluated by simulations and assessed by means of the insensitivity. It will be shown that the proposed PEI-IS does improve the robustness and that it can be easily designed.

Stability analysis of a self‐cycling fermentation model with state‐dependent impulse times

A self‐cycling fermenter is a batch fermenter subject to recurrent emptyings of liquid volume followed by the refilling with new fresh substrate. This article constructs a modified model of self‐cycling fermenter, which is described by an impulsive differential equation at impulse‐dependent times, which have been recently introduced. The main result is a set of conditions depending of the fraction of removed volume, the concentration of new substrate introduced, and the maximal length between two impulses, which ensure the existence and attractiveness of a periodic cycle. A second result provides alternative conditions for the biomass extinction. Copyright © 2013 John Wiley & Sons, Ltd.

Solution examples of an impulse control problem

We study an impulse control problem with switching technology in infinite horizon. We solve the impulse control problem in case of deterministic impulse times on specific transition kernel examples. Our objective is to exhibit an optimal strategy which maximizes the value function in these cases.

An Improved Stabilization Method for Sampled-Data Control Systems With Control Packet Loss

This technical note presents a new method for stability analysis and stabilization of sampled-data systems with control packet loss. It is assumed that if the control packet from the controller to the actuator is lost, then the actuator input to the plant is set to zero. The new method is based on a novel construction of piecewise differentiable Lyapunov functionals by using an impulsive system representation of sampled-data systems. A significant feature of the new Lyapunov functionals is that they are continuous at impulse times but not necessarily positive definite inside the impulse intervals. Applying the new Lyapunov functionals to sampled-data systems with control packet loss, improved criteria for stability and stabilization are derived. The new criteria are proved theoretically to be less conservative than the existing results. Illustrative examples are given which substantiate the usefulness of the proposed method.

Lyapunov formulation of the ISS cyclic-small-gain theorem for hybrid dynamical networks

This paper presents a Lyapunov-based cyclic-small-gain theorem for the hybrid dynamical networks composed of input-to-state stable (ISS) subsystems whose motions may be continuous, impulsive or piecewise constant on the time-line. On the one hand, it is shown that hybrid dynamic networks with interconnection gains less than the identity function are ISS by means of Lyapunov functions. Additionally, an ISS-Lyapunov function for the total network is constructed using the ISS-Lyapunov functions of the subsystems. On the other hand, a novel result of this paper shows that a hybrid dynamic network satisfying the cyclic-small-gain condition can be transformed into one with interconnection gains less than the identity. In sharp contrast with several previously known results, the impulses of the subsystems are time triggered and the impulsive times for different subsystems may be different.

DIFFUSIVE LOGISTIC EQUATIONS WITH TIME DELAY AND IMPULSES: EXISTENCE OF SOLUTION AND ATTRACTORS

A diffusive logistic equation with impulses and single time delay, with zero Robin boundary condition and Holder continuous initial function is studied. The impulses which are continuous functions, occur at fixed times. The magnitude of delay is equal to or less than the difference of any two successive impulse times. The method of upperand lower solution is used for finding the solution. The sufficient conditions for the zero solution to be an attractor of this system is presented. In the case of Neumann boundary condition, existence of positive attractor is proved under certain conditions. DOI : http://dx.doi.org/10.22342/jims.13.1.75.61-72

Robust exponential stability of nonlinear impulsive switched systems with time-varying delays

This paper deals with a class of uncertain nonlinear impulsive switched systems with time-varying delays. A novel type of piecewise Lyapunov functionals is constructed to derive the exponential stability. This type of functionals can efficiently overcome the impulsive and switching jump of adjacent Lyapunov functionals at impulsive switching times. Based on this, a delay-independent sufficient condition of exponential stability is presented by minimum dwell time. Finally, an illustrative numerical example is given to show the effectiveness of the obtained theoretical results.

Designing a Novel Adaptive Impulsive Observer for Nonlinear Continuous Systems Using LMIs

This paper proposes a new class of observers, called adaptive impulsive observer (AIO). AIO is capable to give continuous estimation for the states of a continuous nonlinear system by using the output of the system just at discrete impulse times. This is very significant in applications when establishing a continuous link (couple) between system (drive) and observer (response) is impossible. Also, the AIO estimates both states and unknown parameters of the uncertain system while its computational expense is relatively small in comparison with most conventional observers. Through a new theorem asymptotic convergence of the state estimation error is proved and an upper bound on the maximum possible impulse interval is given. The AIO design routine is simplified by modifying conditions of the proposed theorem to a set of linear matrix inequalities (LMIs). Because of these advantages, the AIO is used through a chaotic systems observer-based synchronization scheme. Simulation results confirm the proficiency of the AIO even when the coupling signal is scalar.

Existence and uniqueness of stochastic differential equations with random impulses and Markovian switching under non-lipschitz conditions

In the paper, stochastic differential equations with random impulses and Markovian switching are brought forward, where the so-called random impulse means that impulse ranges are driven by a series of random variables and impulse times are a random sequence, so these equations extend stochastic differential equations with jumps and Markovian switching. Then the existence and uniqueness of solutions to such equations are investigated by employing the Bihari inequality under non-Lipschtiz conditions.

Minimal Nonnegative Solution of Nonlinear Impulsive Differential Equations on Infinite Interval

The cone theory and monotone iterative technique are used to investigate the minimal nonnegative solution of nonlocal boundary value problems for second-order nonlinear impulsive differential equations on an infinite interval with an infinite number of impulsive times. All the existing results obtained in previous papers on nonlocal boundary value problems are under the case of the boundary conditions with no impulsive effects or the boundary conditions with impulsive effects on a finite interval with a finite number of impulsive times, so our work is new. Meanwhile, an example is worked out to demonstrate the main results.

Existence, continuation, and uniqueness problems of stochastic impulsive systems with time delay

This paper studies stochastic impulsive systems with time delay, where the impulse times are state-dependent. Using Itô calculus, we develop the essential foundation of the theory of the mentioned system. In particular, we establish results on local and global existence, forward continuation, and uniqueness of adapted solutions.

Feedback-reversibility and reachability of linear impulsive systems

For a linear impulsive system, the set of states that are reachable from the origin when the initial time, impulse times, and final time are fixed is contained in an invariant subspace determined by the system data. It is known that reversibility of the system is sufficient to yield, for a specified initial time, the existence of some impulse time set and final time for which the reachable set equals the invariant subspace. In this paper, we relax the reversibility requirement and present a condition that is necessary as well as sufficient under which this property holds. This new condition involves the property of achieving reversibility via feedback and admits an explicit geometric characterization. Moreover, this feedback-reversibility property only needs to hold for the subsystem defined as the full system restricted to the invariant subspace. We further show that feedback-reversibility of the restricted system ensures that the reachable set equals the invariant subspace for almost any impulse time set and final time for which the number of impulse times contained in the underlying time interval exceeds a lower bound.

Research on electronic process of impulse degradation of ZnO-based ceramics

The electrical and dielectric properties of a commercial ZnO-based varistor ceramics were measured in the process of 8/20 μs impulse current degradation up to 5000 times of impulses. The characteristics of U-I in the region of low current and the loss tangent were mainly investigated. It was found that the varistor voltage U1mA will first increase rapidly with impulse times increasing, and then remain stable and finally decrease sharply. Furthermore, a new loss peak emerges at -100℃ in the dielectric spectra after 600 times of impulse degradation, which suggests a new trapping behavior introduced in the degradation process. Activation energy of the new peak first decreases, then becomes independent on impulse times. It was also found that the non-linear coefficient was more sensitive to the degradation process than varistor voltage U1mA. These phenomena have not been reported before, which revealed that the variation of the neutral Fermi level between positive bias Schottky barrier region and reverse bias Schottky barrier region is the origin which leads to the degradation of electrical properties.

Optimal control of impulsive Volterra equations with variable impulse times

We obtain necessary conditions of optimality for impulsive Volterra integral equations with switching and impulsive controls, with variable impulse time-instants. The present work continues and complements our previous work on impulsive Volterra control with fixed impulse times.

State feedback stabilization of linear impulsive systems

We address the fundamental problem of state feedback stabilization for a class of linear impulsive systems featuring arbitrarily-spaced impulse times and possibly singular state transition matrices. Specifically, we show that a strong reachability property enables a state feedback law to be constructed that yields a uniformly exponentially stable closed-loop system. The approach adopts a receding horizon strategy involving a weighted reachability gramian in a manner reminiscent of well-known results for time-varying linear systems for both continuous and discrete-time cases.

Thermal transitions and heat‐sealing of glycerol‐plasticized whey protein films

AbstractTransparent, flexible whey protein‐based edible films plasticized with glycerol were produced by wet (solution‐casting) and dry (twin‐screw extrusion followed by compression‐molding) processes. The relationship between the thermal transitions and the heat‐sealability of the whey protein‐based edible films was investigated. Differential Scanning Calorimetry showed the existence of endothermic peaks with an onset transition temperature of 156.3 ± 1.4°C for both the solution‐cast and extruded films. Films were heat‐sealed using an impulse heat‐sealer at an effective jaw pressure of 293.31 kPa, a voltage of 15 V and a cooling time of 4 s. Various impulse times, ranging from 1.5 to 2.5 s, were used to heat‐seal the films. A thermocouple was used to measure the heat‐sealing temperatures at each impulse time. Heat‐sealing temperatures ranged between 126.1 ± 9.0 and 204.0 ± 5.4°C for the shortest and longest impulse times, respectively. Seal strengths were determined using an Instron Universal Testing Machine. Film thickness appeared to have an effect on seal strength; higher strengths were achieved for thinner films, which, in this case, were the solution‐cast films. Thicker (extruded) films required a longer minimum impulse time to achieve a heat‐seal. The highest seal strength (433.07 ± 39.37 N/m) was obtained with solution cast films (thickness of 0.13 ± 0.01 mm) sealed with an impulse time of 2 s (164.6 ± 5.1°C). Impulse times above 2.5 s (204.0 ± 5.4°C) resulted in degradation of both solution‐cast and extruded films. Copyright © 2009 John Wiley & Sons, Ltd.

Existence of solutions of nth order impulsive integro-differential equations in Banach spaces

In this paper, we prove the existence of solutions of initial value problems for nth order nonlinear impulsive integro-differential equations of mixed type on an infinite interval with an infinite number of impulsive times in Banach spaces. Our results are obtained by introducing a suitable measure of noncompactness.

Exponential stability of impulsive systems with application to uncertain sampled-data systems

We establish exponential stability of nonlinear time-varying impulsive systems by employing Lyapunov functions with discontinuity at the impulse times. Our stability conditions have the property that when specialized to linear impulsive systems, the stability tests can be formulated as Linear Matrix Inequalities (LMIs). Then we consider LTI uncertain sampled-data systems in which there are two sources of uncertainty: the values of the process parameters can be unknown while satisfying a polytopic condition and the sampling intervals can be uncertain and variable. We model such systems as linear impulsive systems and we apply our theorem to the analysis and state-feedback stabilization. We find a positive constant which determines an upper bound on the sampling intervals for which the stability of the closed loop is guaranteed. The control design LMIs also provide controller gains that can be used to stabilize the process. We also consider sampled-data systems with constant sampling intervals and provide results that are less conservative than the ones obtained for variable sampling intervals.

Initial value problems for first order impulsive integro‐differential equations of Volterra type in Banach spaces

In this paper, we use a new method and combining the partial ordering method to study the existence of the solutions for the first order nonlinear impulsive integro‐differential equations of Volterra type on finite interval in Banach spaces and for the first order nonlinear impulsive integro‐differential equations of Volterra type on infinite interval with infinite number impulsive times in Banach spaces. By introducing an interim space and using progressive estimation method, some restrictive conditions on impulsive terms, used before, such as, prior estimation, noncompactness measure estimations are deleted.

Existence of periodic solution for a harvested system with impulses at variable times

In this Letter, a mathematical model for the impulsive exploitation of a single species is proposed and analyzed. An impulsive harvested population model at variable times is investigated, and the sufficient and necessary conditions for the existence of periodic solution are established. We find that the system has a unique nontrivial periodic solution if and only if the initial value and the impulsive times satisfy some conditions specifically, which assure that density of the single species is a periodic surge. A numerical example is presented to illustrate the efficiency of the proposed results.