非线性滞后It(?)随机系统的滞后无关均方渐近稳定性

研究非线性滞后Ito随机系统的滞后无关均方渐近稳定性,将关于线性时滞不等式的Halanay不等式推广到非线性情形,用Lyapunov函数和关于时滞随机系统的比较原理,得到了非线性滞后Ito随机系统滞后无关均方渐近稳定性的一些判据。     

Delay‐range‐dependent control of nonlinear time‐delay systems under input saturation

This paper describes a delay‐range‐dependent local state feedback controller synthesis approach providing estimation of the region of stability for nonlinear time‐delay systems under input saturation. By employing a Lyapunov–Krasovskii functional, properties of nonlinear functions, local sector condition and Jensen's inequality, a sufficient condition is derived for stabilization of nonlinear systems with interval delays varying within a range. Novel solutions to the delay‐range‐dependent and delay‐dependent stabilization problems for linear and nonlinear time‐delay systems, respectively, subject to input saturation are derived as specific scenarios of the proposed control strategy. Also, a delay‐rate‐independent condition for control of nonlinear systems in the presence of input saturation with unknown delay‐derivative bound information is established. And further, a robust state feedback controller synthesis scheme ensuring L₂ gain reduction from disturbance to output is devised to address the problem of the stabilization of input‐constrained nonlinear time‐delay systems with varying interval lags. The proposed design conditions can be solved using linear matrix inequality tools in connection with conventional cone complementary linearization algorithms. Simulation results for an unstable nonlinear time‐delay network and a large‐scale chemical reactor under input saturation and varying interval time‐delays are analyzed to demonstrate the effectiveness of the proposed methodology. Copyright © 2015 John Wiley & Sons, Ltd.     

一类时滞非线性控制系统的输出调节

研究了一类单输出时滞线性系统的输出调节问题,首先通过精确线性化方法将其转化为一类特殊线性时滞系统对非线系统的跟踪总是,然后通过积分变换转化为无时滞的线性系统对非线性系统的跟踪,新的精确线性化结果保证了经过积分变换后的系统仍然可控,同时,提出了可解性的概念解决了线性系统对非线性系统的跟踪问题,得到了时滞非线性系统输出调节问题的局部和全局的结果,该结果对外部系统假设较弱。     

A discretization method for nonlinear delayed non-affine systems

The input time delay is always existent in the practical systems. Analysis of the delay phenomenon in a continuous-time domain is sophisticated. It is appropriate to obtain its corresponding discrete-time model for implementation via digital computer. This paper proposes a new discretization method for calculating a sampled-data representation of nonlinear time-delayed non-affine systems. The proposed scheme provides a finite-dimensional representation for nonlinear systems with non-affine time-delayed input enabling existing nonlinear controller design techniques to be applied to them. The performance of the proposed discretization procedure is evaluated by using a nonlinear system with non-affine time-delayed input. For this nonlinear system, various time delay values are considered.     

一类非线性时滞系统的稳定化控制器设计研究

针对一类单控制滞后的非线性时滞系统,利用非线性状态变换的方法进行非线性变 换,得到一线性时滞系统模型;然后利用一带控制记忆的积分变换进行精确无滞后化变换,得 到一无滞后的线性能控标准型系统,从而利用分步设计的思想.实现非线性时滞系统的稳定 化控制.一数值例子的仿真研究说明了该方法的有效性.     

一类非线性广义系统的时滞相关耗散控制

针对一类带有非线性摄动的广义时滞系统,研究了时滞相关的鲁棒耗散问题.讨论了此类非线性广义时滞系统的鲁棒耗散性.同时对此类非线性广义时滞系统的二次稳定性进行了研究,分别用线性矩阵不等式（LMI）的方法给出了充分条件,也给出了时滞相关的鲁棒耗散的时滞上界.并且,给出了时滞相关的鲁棒耗散的状态反馈控制器.最后,通过例子验证了定理的可行性.     

Sliding mode control design for uncertain time‐delay systems subjected to a class of nonlinear inputs

A sliding mode controller is developed for uncertain time‐delay systems with a class of nonlinear inputs. Two main results are derived in this paper. The first result is the presentation of a new delay‐dependent stability condition of uncertain time‐delay systems. In a comparison example, this stability condition is shown to be less conservative than the ones reported recently. The second result is to present a new sliding mode control for uncertain time‐delay systems subjected to a class of nonlinear inputs. The stability of time‐delay systems with unmatching condition in the sliding mode is also discussed. Two illustrative examples are included to demonstrate the superiority of the obtained results. Copyright © 2003 John Wiley & Sons, Ltd.     

Robust Exponential Stability and Stabilization of a Class of Nonlinear Stochastic Time‐Delay Systems

This paper presents new exponential stability and delayed‐state‐feedback stabilization criteria for a class of nonlinear uncertain stochastic time‐delay systems. By choosing the delay fraction number as two, applying the Jensen inequality to every sub‐interval of the time delay interval and avoiding using any free weighting matrix, the method proposed can reduce the computational complexity and conservativeness of results. Based on Lyapunov stability theory, exponential stability and delayed‐state‐feedback stabilization conditions of nonlinear uncertain stochastic systems with the state delay are obtained. In the sequence, the delayed‐state‐feedback stabilization problem for a nonlinear uncertain stochastic time‐delay system is investigated and some sufficient conditions are given in the form of nonlinear inequalities. In order to solve the nonlinear problem, a cone complementarity linearization algorithm is offered. Mathematical and/or numerical comparisons between the proposed method and existing ones are demonstrated, which show the effectiveness and less conservativeness of the proposed method.     

A constructive approach for an optimal control applied to a class of nonlinear time delay systems

In this contribution, we obtain a nonlinear controller for a class of nonlinear time delay systems, by using the inverse optimality approach. We avoid the solution of the Hamilton Jacobi Bellman type equation and the determination of the Bellman's functional by extending the inverse optimality approach for delay free nonlinear systems to time delay nonlinear systems. This is achieved by combining the Control Lyapunov Function framework and Lyapunov-Krasovskii functionals of complete type. Explicit formulas for an optimal control are obtained. The efficiency of the proposed method is illustrated via experimental results applied to a dehydration process whose model includes a delayed state linear part and a delayed nonlinear part. To give evidence of the good performance of the proposed control law, experimental comparison against an industrial Proportional Integral Derivative controller and optimal linear controller. Additionally experimental robustness tests are presented.     

Global adaptive regulation of feedforward nonlinear time‐delay systems by output feedback

The problem of global adaptive state regulation is investigated via output feedback for uncertain feedforward nonlinear time‐delay systems. Compared with existing results, our control schemes can be applicable to more general nonlinear time‐delay systems because of combining the low‐gain scaling approach with the backstepping method. In particular, we allow that there exist uncertain output function and uncertain growth rate imposed on nonlinear terms. Also, one considers a class of nonlinear systems with main‐axis delay. By the Lyapunov–Krasovskii theorem, delay‐independent controllers are proposed by constructing novel low‐gain observers driven by system input, to regulate the states of original system while all the closed‐loop signals are globally bounded. Furthermore, two examples are given to illustrate the usefulness of our results. Copyright © 2016 John Wiley & Sons, Ltd.     

具有时滞的不确定鲁里叶控制系统的绝对鲁棒稳定性

讨论了具有时滞的非线性不确定鲁里叶控制系统的鲁棒绝对稳定性问题,应用Bellman-Gronwell不等式和Lyapunov泛函方法研究了不确定鲁里叶控制系统的鲁棒绝对稳定性并给出了系统的滞相关稳定和时滞无关稳定的充分判据,运用这些条件可以直接估计具有时滞的非线性不确定鲁里叶控制系统的鲁棒绝对稳定界和时滞界。     

非线性时滞系统的稳定性分析及鲁棒稳定性条件

研究非线性时滞系统的稳定性.应用Lyapunov函数,分别讨论确定性和不确定性 非线性时滞系统.对于确定性系统,给出其零解渐近稳定的充分条件;对于不确定性系统,给 出其零解鲁棒稳定的充分条件.最后通过两个实例说明所给方法的有效性.     

非线性关联不确定变时滞系统的鲁棒绝对稳定控制

采用积分不等式，研究了一类具有状态和输入变时滞的非线性关联不确定系统的鲁棒综合问题．基于线性矩阵不等式（LMI）分别导出了具有扇形角约束和范数有界约束的两类非线性关联不确定系统的线性无记忆状态反馈控制律设计方法，该方法不要求系统的两输入项对系统完全可控．数值实例说明了本文方法的有效性．     

Simultaneous compensation of input and state delays for nonlinear systems

The problem of compensation of arbitrary large input delay for nonlinear systems was solved recently with the introduction of the nonlinear predictor feedback. In this paper we solve the problem of compensation of input delay for nonlinear systems with simultaneous input and state delays of arbitrary length. The key challenge, in contrast to the case of only input delay, is that the input delay-free system (on which the design and stability proof of the closed-loop system under predictor feedback are based) is infinite-dimensional. We resolve this challenge and we design the predictor feedback law that compensates the input delay. We prove global asymptotic stability of the closed-loop system using two different techniques—one based on the construction of a Lyapunov functional, and one using estimates on solutions. We present two examples, one of a nonlinear delay system in the feedforward form with input delay, and one of a scalar, linear system with simultaneous input and state delays.     

非线性时滞系统的稳定性分析及 鲁棒稳定性条件1)

研究非线性时滞系统的稳定性.应用Lyapunov函数,分别讨论确定性和不确定性非线性时滞系统.对于确定性系统,给出其零解渐近稳定的充分条件;对于不确定性系统,给出其零解鲁棒稳定的充分条件.最后通过两个实例说明所给方法的有效性.     

非线性参数扰动多重时滞系统的鲁棒稳定性分析与变结构控制

研究一类非线性参数扰动满足范数有界条件的多重时滞系统,利用Ｌｙａｐｕｎｏｖ函数方法,获得了一个新的鲁棒稳定性充分条件,并应用变结构控制实现了该类非线性参数扰动多重时滞系统的鲁棒镇定。     

Adaptive observers for time-delay nonlinear systems in triangular form

A simple nonlinear observer with a dynamic gain is proposed for a class of bounded-state nonlinear systems subject to state delay. By saturating the states of the observer nonlinearities with either symmetric or non-symmetric saturation functions, we show that the observer exists, whatever the delay is. Furthermore, it will be highlighted that the observer design is free from any preliminary analysis of the time-delay system such as estimating the Lipschitz constants of nonlinearities. The proposed design encompasses a wide class of nonlinear and time-delay systems written in triangular form and generalizes previous results on delayless nonlinear systems.     

Frequency-domain estimates of the sampling interval in multirate nonlinear systems by time-delay approach

A class of nonlinear hybrid systems consisting of a continuous plant and a multirate sampled-data controller is considered. Applying the time-delay approach, the system is transformed to the system with a time-varying sawtooth delay. Then, the value of the sampling intervals ensuring stability of the closed-loop system is estimated based on the frequency-domain circle-like criterion for systems with time-varying delay. Such a criterion for multirate MIMO systems is established based on the previous result for SISO systems proposed by M.Churilova in 1995. Efficiency and advantages of the method are illustrated by numerical examples. The key advantage of the proposed approach is that it is applicable to multirate systems nonaffine in control. It allows one to use a nonlinear feedback for stabilisation. Particularly, the case of nonsmooth or discontinuous nonlinear systems can be treated.     

Approximate feedback linearization of a class of nonlinear systems with time-varying delays in states via matrix inequality

In this paper, feedback linearization method is proposed for nonlinear systems with a time varying delay in states. The diffeomorphism is presented to linearize the state-delayed nonlinear system if time-varying delay is known. Furthermore, we propose a control scheme to stabilize the approximate feedback linearizable system under the proposed conditions if the first order derivative of timevarying delay and the parametric uncertainties are finite and measurable.     

Disturbance decoupling for time delay systems

In this paper the disturbance decoupling problem associated with a class of linear and nonlinear time delay systems is considered. The solution to this problem is given in terms of the relative degrees associated with the input and the disturbance of the corresponding time delay systems. A stability study using some results due to Pontryagin is presented for the resultant closed-loop system when the delay system is linear. Also, an approximate causal solution is proposed for the nonlinear time delay system based on its linearization around an equilibrium point. © 1997 by John Wiley & Sons, Ltd.