Linear Systems Subject to Input Saturation and Time Delay: Global Asymptotic Stabilization

This note deals with the problem of global asymptotic stabilization of linear systems by bounded static feedbacks subject to time delay. Under standard necessary conditions, we provide two constructions of controllers of nested saturation type which extends to the general case partial results of previous papers for arbitrary small bound on the control and large (constant) delay. To validate the approach, a third-order integrator and oscillator with multiplicity two example is presented     

VOIP动态缓出时延算法研究分析

在以包为单位进行数据传输合、语音应用程序(VOIP,Voice Over Internet Protocol)中,为了补偿数据包在网络传输中不可预知的网络传输延迟,在接收端首先必须把接收到的数据包缓存起来,缓存一定的时间再播放出来,以减少通话的抖动,得到比较满意的通话质量。文章主要研究动态缓出时延算法,力求使这个缓出时延尽可能小,同时尽可能减少包的丢失率。文章提出了一个有效动态缓出时延算法,该算法主要跟踪最近到达的数据包的网络传输时延求出其近似分布函数,并利用这些信息和延迟峰的侦测算法预测下一个语音峰的缓出时延。实验结果表明利用该算法可以在缓出时延和包丢失率之间达到最佳平衡,是一种理想、有效的算法。     

Asymptotic series solution of singularly perturbed optimal control problems

An optimal control problem of some nonlinear differential equations containing a small parameter is considered. This problem leads to a two-point boundary value problem (TPBVP) whose differential order can be reduced by neglecting the small parameter. In this paper an explicit method of constructing an asymptotic power series solution of the TPBVP as the small parameter tends to zero is presented. The method allows a separation of slow and fast dynamics in the problem while reducing the differential order of the equations. The determination of asymptotic series terms is computationally simple since one needs to solve only initial or final value problems instead of TPBVP's. The method has computational similarities with quasilinearization and second variation techniques.     

时滞神经网络的全局渐近稳定性分析

研究一类具有时滞的细胞神经网络的稳定性问题,利用Lyapunov—Krasovskii泛函的方法,给出时滞相关的稳定性判据。稳定性判据是以线性矩阵不等式的形式给出,可以很容易得出时滞的上界。在得到时滞相关的稳定性判据的同时也可以得到时滞无关的稳定性判据。数值算例说明其结果的优越性。     

Robust stability of multiple-time-delay uncertain systems with series nonlinearities

This paper considers the problem of output feedback stabilization of multiple time delay uncertain systems with series nonlinearities. We develop a delay-dependent method for designing linear dynamic output feedback controllers which ensures global uniform asymptotic stability for the range of allowable delay times. The proposed stabilization method, which is based on the comparison theorem and some analytical methods, is employed to treat this problem. The most striking feature of the results presented is their simplicity in testing the stabilization of multiple-time-delay systems with series nonlinearities and this can be used to estimate the size of the delay time. Examples are used to illustrate the less conservative results of the proposed methods compared with existing methods in the literature.     

Robust predictive extended state observer for a class of nonlinear systems with time-varying input delay

ABSTRACT

This paper deals with asymptotic stabilisation of a class of nonlinear input-delayed systems via dynamic output feedback in the presence of disturbances. The proposed strategy has the structure of an observer-based control law, in which the observer estimates and predicts both the plant state and the external disturbance. A nominal delay value is assumed to be known and stability conditions in terms of linear matrix inequalities are derived for fast-varying delay uncertainties. Asymptotic stability is achieved if the disturbance or the time delay is constant. The controller design problem is also addressed and a numerical example with an unstable system is provided to illustrate the usefulness of the proposed strategy.     

Asymptotic Stability and Finite‐Time Stability of Networked Control Systems: Analysis and Synthesis

This paper focuses on the problems of asymptotic stability and finite‐time stability (FTS) analysis, along with the state feedback controller design for networked control systems (NCSs) with consideration of both network‐induced delay and packet dropout. The closed‐loop NCS is modeled as a discrete‐time linear system with a time‐varying, bounded state delay. Sufficient conditions for the asymptotic stability and the FTS of the closed‐loop NCS are provided, respectively. Based on the stability analysis results, a mixed controller design method, which guarantees the asymptotic stability of the closed‐loop NCS in the usual case and the FTS of the closed‐loop NCS in the unusual case (that is, in some particular time intervals, large state delay occurs), is presented. A numerical example is provided to illustrate the effectiveness of the proposed mixed controller design method.     

On maximum periodic solutions of integrodifferential equations of volterra type and their stability

Consideration was given to the question of asymptotic (exponential) stability of the maximum periodic solutions of the integrodifferential equations which have an asymptotically stable linear part and small periodic (exponential maximum periodic) perturbation. Under the unlimitedly increasing time, these solutions tend to the periodic modes. The sufficient conditions for asymptotic stability were indicated. In the resonance case where the linearized equation has a pair of purely imaginary roots with the corresponding oscillation frequency coinciding with the oscillation frequency of the periodic part of small perturbation (time function) and the coefficients of the power series expansion of the nonlinear terms, consideration was given to the problem of existence for the maximum periodic solutions of the integrodifferential equation. Conditions were established for existence of such solutions representable by the power series in the fractional degrees of the small parameter characterizing the value of small perturbation in the equation.     

A new criterion of delay-dependent asymptotic stability for Hopfield neural networks with time delay.

In this brief, the problem of global asymptotic stability for delayed Hopfield neural networks (HNNs) is investigated. A new criterion of asymptotic stability is derived by introducing a new kind of Lyapunov-Krasovskii functional and is formulated in terms of a linear matrix inequality (LMI), which can be readily solved via standard software. This new criterion based on a delay fractioning approach proves to be much less conservative and the conservatism could be notably reduced by thinning the delay fractioning. An example is provided to show the effectiveness and the advantage of the proposed result.     

Quantitative robustness measure of uncertain time delay systems vianonsingularity analysis

The objective of this paper is to derive an upper bound for the delay time constant such that a linear uncertain time delay system still keeps its asymptotic stability, if it is nominally stable and the delay time constant remains smaller than the upper bound. The problem is solved by using matrix measure and nonsingularity analysis of matrices, and the results are shown to be less conservative than previous results     

Taylor series expansion based repetitive controllers for power converters,subject to fractional delays

Digital repetitive controllers are widely employed to track/reject the periodic signals with zero steady-state error. Their implementation involves the use of single or multiple digital delay elements. Practically, the delay element is implemented by the use of memory locations, where samples are held and released after a specific number of sampling periods, equivalent to the desired time delay. A problem arises when the desired time delay becomes a non-integer multiple of the sampling time. Such time delays can be accurately realized by employing a fractional delay filterThis paper presents a Taylor Series expansion based digital repetitive controller designed to implement any (integer, non-integer) delay in the control of power converters, occurring due to uncontrollable variations in the reference frequency. The T3644aylor Series expansion transforms the fractional delay filter design problem to a differentiator/sub-filter design. Finite impulse response (FIR) and infinite impulse response (IIR) fractional delay (FD) filter concepts can be applied to realize the required fractional delay. This structure provides efficient on-line tuning capabilities i.e. FD can easily generate any required fractional delay without redesigning the filter when the delay parameter varies. An example is demonstrated to show the effectiveness of this approach, for a single-phase power inverter feeding a passive load.     

Robust H∞ controller design for continuous‐time piecewise time‐delay systems

This paper investigates the robust H_∞ control problem for continuous‐time piecewise time‐delay systems by using piecewise continuous Lyapunov function. The uncertainties of the systems under consideration are expressed in a linear fractional form. A strict linear matrix inequality approach is developed to obtain delay‐dependent asymptotic stability conditions and H_∞ performance. The H_∞ controller design problem is solved by exploiting the cone complementarity linearization (CCL) method. Finally an example is given to illustrate the application of the proposed approach. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Global robust asymptotic stability analysis of uncertain switched Hopfield neural networks with time delay in the leakage term

This paper deals with the problem of delay-dependent global robust asymptotic stability of uncertain switched Hopfield neural networks (USHNNs) with discrete interval and distributed time-varying delays and time delay in the leakage term. Some Lyapunov––Krasovskii functionals are constructed and the linear matrix inequality (LMI) approach are employed to derive some delay-dependent global robust stability criteria which guarantee the global robust asymptotic stability of the equilibrium point for all admissible parametric uncertainties. The proposed results that do not require the boundedness, differentiability, and monotonicity of the activation functions. Moreover, the stability behavior of USHNNs is very sensitive to the time delay in the leakage term. It can be easily checked via the LMI control toolbox in Matlab. In the absence of leakage delay, the results obtained are also new results. Finally, nine numerical examples are given to show the effectiveness of the proposed results.     

H ∞ filtering for stochastic systems with time-varying delay

This article considers the problem of H _∞ filter design for stochastic systems with time-varying delay. The time delay is assumed to be of interval type. Attention is focused on the design of delay-dependent filters that guarantee the asymptotic stability in mean square and a prescribed noise attenuation level in an H _∞ sense for the filtering error dynamics. The delay-dependent H _∞ filter design scheme is proposed in terms of a linear matrix inequality. A numerical example is used to illustrate the effectiveness of the proposed approach.     

Analysis of stability and stabilization of cascade systems with time delay in terms of linear matrix inequalities

The stability of nonlinear cascade systems with a time delay is studied. Conditions of the global asymptotic stability in terms of linear matrix inequalities for a finite set of matrices are obtained. The problem of stabilization of the controlled delay system is considered, which is solved based on the stability conditions. The proposed approach to the analysis of qualitative properties and to the solution of stabilization problems is based on the results concerning the asymptotic stability of the delay linear systems, the decomposition of the original system, and the representation of the delay nonlinear system by a Takagi–Sugeno system. Examples illustrating the simplification of the system analysis by reducing its size and decreasing the number of linear matrix inequalities are discussed.     

Stability conditions of constrained delay systems via positive invariance

A delay system is represented by a linear difference equation. The system parameters and the delays are assumed to be imperfectly known. The output vector is perturbed by an external disturbance vector. The addressed problem is to characterize conditions which guarantee that the output vector remains in a given domain defined by a set of symmetrical linear constraints. This problem is solved by imposing positive invariance conditions. These conditions also imply delay independent asymptotic stability of the associated deterministic system. The possible use of these new robust stability conditions for controlling an input–output delay model is then presented. An application is finally proposed; it concerns an inventory control problem for a simple production loop subject to constraints on inventory levels. © 1998 John Wiley & Sons, Ltd.     

Characteristic measures of switching functions

A basic problem in switching theory is the optimal realizations of switching functions in a certain basis and with respect to a certain characteristic measure such as complexity, circuit cost, number of input terminals, delay time. Naturally this problem has received much attention and although a general solution has not been accomplished, many very good results have been obtained.This survey does not attempt to include all the literature concerning this general problem. Some outstanding and basic papers will be reviewed emphasizing ideas, assumptions, results and limitations. A measure of circuit performance, labeled L(n), a characteristic index of the class of n-variable functions, will be defined. This measure is an important tool for understanding the difficulties of the problem and for obtaining most of the results. This survey reviews the most significant literature on problems concerning characteristic measures of switching functions, and in particular, measures of circuit complexity, formula complexity or length, and delay time required to realize switching functions. The asymptotic and finite behavior, the upper and lower bounds, and the order of magnitude of L(n) are included for each particular case.     

Relaxation oscillations in a system with delays modeling the predator–prey problem

A new asymptotic method for investigating complex relaxation oscillations in a system with delay is offered. By applying it, we can reduce the problem of predator–prey system dynamics to that of one-dimensional maps analysis. Some conclusions of a biological nature based on asymptotic analysis are made.     

Internal model approach to cooperative robust output regulation for linear uncertain time‐delay multiagent systems

In this paper, we study the cooperative robust output regulation problem for linear uncertain multiagent systems with both communication delay and input delay by the distributed internal model approach. The problem includes the leader‐following consensus problem of linear multiagent systems with time delay as a special case. We first generalize the internal model design method to systems with both communication delay and input delay. Then, under a set of standard assumptions, we have obtained the solution to the problem via both the state feedback control law and the output feedback control law. In contrast to the existing results, our results apply to general linear uncertain multiagent systems, accommodate a large class of leader signals, and achieve asymptotic tracking and disturbance rejection at the same time.     

Stability analysis of a rigid robot with output-based controller and time delay

This study considers the problem of stabilizing a rigid robot with an output-based controller and time-delayed input functions applied to the robot joints. We establish sufficient conditions for asymptotic stability of the system under consideration. These conditions are based on well-defined relationships between the magnitude of the controller gains and the time delay factor.