不确定时滞系统的无记忆鲁棒控制

讨论了含有时变时滞以及时变输入控制的 时滞线性系统的鲁棒可镇定性问题,就所有可结构化不确定参数以及所有非结构化不确定参 数两种情形分别得到了系统可由状态反馈控制器镇定的充分条件,并且相应给出了控制器的 设计．     

Exponential dynamic output feedback controller design for stochastic neutral systems with distributed delays

This paper investigates the problem of stochastic stabilization for stochastic neutral systems with distributed delays. The time delay is assumed to appear in both the state and measurement equations. Attention is focused on the design of linear dynamic output feedback controllers such that the resulting closed-loop system is exponentially mean-square stable. A sufficient condition for the solvability of the problem is obtained in terms of a linear matrix inequality (LMI). When this LMI is feasible, an explicit expression of a desired dynamic output feedback controller is also given. The theory developed in this paper is demonstrated via a numerical example.     

Linear and nonlinear stabilizing continuous controllers ofuncertain dynamical systems including state delay

The problem of robust stabilization of a class of time-varying dynamical systems with disturbance, uncertain parameters, and a bounded time-varying state delay is considered. Two classes of stabilizing continuous controllers are proposed. The proposed controllers can guarantee the existence of the solution to the dynamical system in the usual sense and can also be directly implemented in the practical control problems. Moreover, since the proposed controllers are completely independent of the time delay (which is only assumed to be any nonnegative bounded and continuous function), the results developed in this note are applicable to a class of dynamical systems with uncertain time delays. Finally, a numerical example is given to demonstrate the validity of the results     

Synthesis of non-rational controllers for linear delay systems

This paper addresses the control of linear delay systems using non-rational controllers. The structure of the controller is chosen so as to copy the structure of the plant, reproducing the delays in the state and in the output. The resulting stabilization and performance design problems are entirely expressed as linear matrix inequalities. Although the design inequalities are based on delay independent stability conditions, the overall design is delay dependent, in the sense that the controller makes use of the delay parameter of the plant. This parameter is assumed to be constant yet arbitrary. Using non-rational controllers we overcome the main difficulty faced when designing rational controllers for linear delay systems, which is to incorporate in the design problem the matrix multiplier used to prove stability with respect to the delayed part of the system. We illustrate the paper with several examples and provide extensive comparisons with existent results.     

Design of Adaptive Block Backstepping Controllers with Perturbations Estimation for Nonlinear State‐Delayed Systems in Semi‐Strict Feedback Form

This paper is an extended study of an existing block backstepping control scheme designed for a class of perturbed multi‐input systems with multiple time‐varying delays to solve regulation problems, where the time‐varying delays must be linear with state variables. A new control scheme is proposed in this research where all the unknown multiple time‐varying delay terms in the dynamic equations can be nonlinear state functions in non‐strict feedback form, and the upper bounds of the time‐delays as well as their derivatives need not to be known in advance. Another improvement is to further alleviate the problem of “explosion of complexity,” i.e., to reduce the number of time derivatives of virtual inputs that the designers have to compute in the design of controllers. This is done by utilizing an existent derivative estimation algorithm to estimate the perturbations in the designing of proposed controllers. Adaptive mechanisms are also embedded in the controllers so that the upper bounds of perturbations and perturbation estimation errors are not required to be known beforehand. The resultant controlled systems guarantee asymptotic stability in accordance with the Lyapunov stability theorem. Finally, a numerical example and a practical application are demonstrated to verify the merits and feasibility of the proposed control scheme.     

具有短时延的网络控制系统的一种鲁棒控制方法

针对具有短时延的网络控制系统, 本文提出了一种基于鲁棒控制的方法来解决该类系统的稳定化控制问题. 考虑状态反馈控制律, 将闭环网络控制系统描述为一个离散时间线性不确定系统模型, 其中的不确定部分反映了时延的时变特性对系统动态的影响. 得到了该闭环网络控制系统的渐近稳定性条件, 且该条件建立了闭环网络控制系统稳定性与两个时延参数, 即允许时延上界和允许时延变换范围, 之间的定量关系. 进一步的, 还给出了稳定化反馈控制器的设计步骤. 最后通过一个示例验证了本文所提出方法的有效性.     

带传输滞后的线性离散系统的状态反馈镇定

针对存在传输滞后的线性离散系统的状态反馈镇定问题,给出了系统可镇定的一个内部限制条件.为克服这一限制条件,提出了两种方法:一种是充分利用滞后状态的信息,另一种是设计带有递推动态的状态反馈控制器.研究结果表明,若系统在没有传输滞后时能通过状态反馈被镇定,则存在传输滞后时一定也能通过设计新的控制器使系统被镇定.     

H∞-output feedback controller design for linear systems withtime-varying delayed state

This paper considers the H∞-controller design problem for linear systems with time-varying delays in states. The authors obtain sufficient conditions for the existence of H∞ controllers in terms of three linear matrix inequalities (LMIs). These sufficient conditions are dependent on the maximum value of the time derivative of time-varying delay. Furthermore, they briefly explain how to construct such controllers from the positive-definite solutions of their LMIs and give an example     

H ∞ output-feedback control for switched linear discrete-time systems with time-varying delays

In this paper, the problem of H _∞ output feedback control for switched linear discrete-time systems with time delays is investigated. The time delay is assumed to be time-varying and bounded. By constructing a switched quadratic Lyapunov function for the underlying system, both static and dynamic H _∞ output feedback controllers are designed respectively such that the corresponding closed-loop system under arbitrary switching signals is asymptotically stable and a prescribed H _∞ noise-attenuation level bound is guaranteed. A cone complementary linearization algorithm is exploited to design the controllers. A numerical example is presented to show the effectiveness of the developed theoretical results.     

Dynamic control of systems with variable state-delay

The problem of designing dynamic controllers for a class of linear dynamical systems with time-varying delays subject to input disturbance as well as output measurement error and in which some parameters are unknown-but-bounded is considered. It is establishing that when certain structural constraints are met, then two stabilizing controllers can be constructed to render the closed-loop system ‘globally practically stable’. The controllers have three terms: a growth term, an output-driven term and a nonlinear term. Robustness of the developed dynamic controllers against mismatched uncertainties is also proved. Simulation studies are carried out on a water-quality model to illustrate the potential of the control methodology.     

Output feedback guaranteed cost control of networked linear systems with random packet losses

This article is concerned with the output feedback guaranteed cost control problem for a class of networked control systems (NCSs) with both packet losses and network-induced delays. The packet-loss processes in the forward channel and the backward channel are modelled as two Markov chains. The dynamic output feedback controllers are considered, and the closed-loop NCS is modelled as a discrete-time Markovian system with two modes and unit time delay. By using a properly constructed Lyapunov function and the state transformation technique, a sufficient condition is derived for the closed-loop NCS to be mean-square exponentially stable and ensure a decay rate that can be tuned according to the packet loss situations in the networks. Moreover, design procedures for the guaranteed cost controllers are also presented based on the obtained stability condition and guaranteed cost performance result. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed results.     

Stabilizing controllers using observers for uncertain systems with delays

In this paper, we study the problem of designing stabilizing controllers using observers for a class of uncertain systems with state and input delays. The uncertainties are assumed to be norm bounded. By employing a Lyapunov-Krasovskii functional approach, it is proven that the closed-loop observer-based controlled system is asymptotically stable. The observer and state feedback controllers are determined by solving two linear matrix inequalities which are independent of the delay factors. A simulation example is given to illustrate the theoretical developments.     

A switching system approach to actuator assignment with limited channels

The problem of integrated design of controller and communication sequences is addressed for networked control systems with simultaneous consideration of medium access limitations and network‐induced delays, packet dropouts and measurement quantization. By exploiting a Lyapunov–Krasovskii functional and by making use of novel techniques for switching delay systems, it is shown that linear time invariant systems can be stabilized with delay‐dependent state feedback controllers and communication sequences satisfying appropriate delay‐dependent conditions in terms of linear matrix inequalities. Illustrative examples are provided to show the usefulness and advantage of the developed results. Copyright © 2009 John Wiley & Sons, Ltd.     

一种带有动态输出反馈控制器的网络控制系统的Markov跳变模型

对于网络控制系统(Networked control systems, NCS)中的随机延迟时变有界, 其上界大于一个采样周期的情况, 建立了带有动态输出反馈控制器的连续时间系统模型. 以此为基础, 应用连续时间系统模型离散化与增广状态空间方法, 建立了受控于有限状态Markov链的离散时间跳变系统模型. 在该系统的稳定性控制器设计中, 给出了一种求内点法的初始可行解的方法, 从而解决了所建模型的可解性问题. 理论分析和车载倒立摆上的仿真计算表明, 由上述模型与改进算法所给出的动态输出反馈控制器能使系统稳定.     

不确定性时滞大系统的分散鲁棒H∞控制

研究一类具有状态时滞的内联不确定性动态大系统的分散鲁棒H∞控制问题.系统 的不确定性参数满足范数有界条件.得到了由无记忆状态反馈分散控制器使每一个子系统和 整个大系统都可镇定且满足给定H∞性能的充分条件.所得结果与系统时滞的大小有关,并 以线性矩阵不等式的形式给出.     

Stability domains of the delay and PID coefficients for general time-delay systems

Time delays are encountered in many physical systems, and they usually threaten the stability and performance of closed-loop systems. The problem of determining all stabilising proportional-integral-derivative (PID) controllers for systems with perturbed delays is less investigated in the literature. In this study, the Rekasius substitution is employed to transform the system parameters to a new space. Then, the singular frequency (SF) method is revised for the Rekasius transformed system. A novel technique is presented to compute the ranges of time delay for which stable PID controller exists. This stability range cannot be readily computed from the previous methods. Finally, it is shown that similar to the original SF method, finite numbers of singular frequencies are sufficient to compute the stable regions in the space of time delay and controller coefficients.     

Optimal guaranteed cost control of a class of hybrid systems with mode-dependent mixed time delays

In this paper, the guaranteed cost control problem is investigated for a class of nonlinear systems with Markovian jumping parameters and mixed time delays. The time delays involved consist of the mode-dependent discrete time delay and the distributed time delay with mode-dependent upper and lower boundaries; the associated cost function is a quadratic function, and nonlinear functions are assumed to satisfy sector-bounded conditions. By introducing new Lyapunov–Krasovskii functionals and some analytic techniques, the sufficient conditions for the existence of guaranteed cost controllers are derived for the systems and related cost function. Moreover, a linear matrix inequality (LMI) based approach to design the optimal guaranteed cost controller is formulated to minimise the guaranteed cost of the closed-loop system. Numerical simulation is further carried out to demonstrate the effectiveness of the proposed methods.     

基于Riccati-It方程设计线性时滞系统鲁棒控制器的方法

利用Riccati-Ito型矩阵代数方程研究线性时不变系统的状态反馈镇定问题，对时滞系统给出了一种状态反馈镇定方法，这种镇定方法适应于许多时滞系统，其设计方案具有滞后无关性及对于许多系统滞后项系数任意性的完全适应性．本文第二部分研究时不变线性不确定系统的鲁棒镇定，利用Riccati-Ito型矩阵代数方程给出了这类系统鲁棒镇定控制器的设计方法．     

Delay compensation for linear systems with both state and distinct input delays

This paper is concerned with the stabilization of linear systems with both state and distinct input delays. Nested predictor feedback controllers are designed to predict the future states such that the distinct input delays that can be arbitrarily large yet bounded are compensated completely. It is shown that the compensated closed‐loop system possesses the same characteristic equation as the closed‐loop system without distinct input delays. Both continuous‐time and discrete‐time time‐delay systems are studied in this paper. Moreover, the safe implementation problem for the continuous‐time nested predictor feedback controller is solved via adding input filters. Three numerical examples show the effectiveness of the proposed approaches.     

Stabilisation and consensus of linear systems with multiple input delays by truncated pseudo-predictor feedback

This paper provides a new approach referred to as pseudo-predictor feedback (PPF) for stabilisation of linear systems with multiple input delays. Differently from the traditional predictor feedback which is from the model reduction appoint of view, the proposed PPF utilises the idea of prediction by generalising the corresponding results for linear systems with a single input delay to the case of multiple input delays. Since the PPF will generally lead to distributed controllers, a truncated pseudo-predictor feedback (TPPF) approach is established instead, which gives finite dimensional controllers. It is shown that the TPPF can compensate arbitrarily large yet bounded delays as long as the open-loop system is only polynomially unstable. The proposed TPPF approach is then used to solve the consensus problems for multi-agent systems characterised by linear systems with multiple input delays. Numerical examples show the effectiveness of the proposed approach.