Lurie控制系统的关联绝对稳定性-双线性矩阵不等式方法

研究任意两个相互独立的Lurie控制系统能否通过关联或协调控制组成绝对稳定大系统的问题,给出两个Lurie控制系统可关联绝对稳定的充分条件,并给出了计算关联矩阵的双线性矩阵不等式方法.研究结果表明:两个非绝对稳定的系统可以通过关联或协调控制来实现关联大系统的绝对稳定性,取消了大系统稳定性分析中对关联的不合理限制.文末给出了本文结果的数值例子.     

Robust absolute stability of Lurie interval control systems

This paper considers robust absolute stability of Lurie control systems. Particular attention is given to the systems with parameters having uncertain, but bounded values. Such so‐called Lurie interval control systems have wide applications in practice. In this paper, a number of sufficient and necessary conditions are derived by using the theories of Hurwitz matrix, M matrix and partial variable absolute stability. Moreover, several algebraic sufficient and necessary conditions are provided for the robust absolute stability of Lurie interval control systems. These algebraic conditions are easy to be verified and convenient to be used in applications. Three mathematical examples and a practical engineering problem are presented to show the applicability of theoretical results. Numerical simulation results are also given to verify the analytical predictions. Copyright © 2007 John Wiley & Sons, Ltd.     

Absolute stability of Lurie networked control systems

This paper is concerned with the absolute stability problem of networked control systems (NCSs) with the controlled plant being Lurie systems (Lurie NCSs), in which the network‐induced delays are assumed to be time‐varying and bounded. First, in consideration of both the time‐varying network‐induced delays and data packet dropouts, the Lurie NCSs can be modeled as a multiple‐delays Lurie system. Then, a delay‐dependent absolute stability condition is established by using the Lyapunov–Krasovskii method. Next, two approaches to controller design are proposed in the terms of simple algebra criteria, which are easily solved via the toolbox in Matlab. Furthermore, the main results can be extended to robust absolute stability of Lurie NCSs with the structured uncertainties, where robust absolute stability conditions and approaches to robust controller design are presented. Finally, two numerical examples are worked out to illustrate the feasibility and the effectiveness of the proposed method. Copyright © 2009 John Wiley & Sons, Ltd.     

关联 Lurie 控制大系统的参数绝对稳定性

针对一类具有不确定性参数和参考输入的关联 Lurie 大系统, 研究其参数绝对稳定性的问题, 即同时考虑参数变化引起的平衡点的改变及其稳定性的问题. 首先, 基于分散状态反馈, 研究了当不确定性参数变化和参考输入改变时, 关联 Lurie 大系统参数稳定性存在条件和参数稳定区域. 其次, 给出了在该参数稳定区域中基于矩阵不等式条件的关联大系统稳定性存在的线性矩阵不等式 (LMI) 条件. 最后, 研究了多胞型关联 Lurie 大系统参数绝对稳定性存在的充分条件和求解算法. 仿真例子说明了方法的有效性.     

具有多个独立执行机构的Lurie控制系统的鲁棒绝对稳定性

本文讨论了具有多个相互独立执行机构的Lurie型区间直接控制系统和区间间接控制系统的绝对稳定性 ,给出了系统稳定的若干充分条件 ,对文 [5 ]所讨论的问题作了进一步探讨 .     

Lurie系统的鲁棒量化控制

研究了Lurie系统的鲁棒量化状态反馈控制问题, 其中的量化器为静态对数量化器. 首先, 根据Lurie系统自身特点以及对数量化器的特性, 将量化状态反馈控制作用下的Lurie系统建模成具有两个扇形约束的不确定系统. 然后分别考虑了没有量化和有量化作用两种情形, 利用小增益定理, 得到了闭环系统内稳定的充分必要条件, 并进一步给出了相应的状态反馈控制律. 最后, 数值例子表明了本文方法的有效性.     

Robust H∞ Sliding Mode Control for a Class of Singular Stochastic Nonlinear Systems

This paper concerns the problem of robust H_∞ sliding mode control for a class of singular stochastic nonlinear systems. Integral sliding mode control is developed to deal with this problem. Based on the integral sliding surface of the design and linear matrix inequality, a sufficient condition which guarantees the sliding mode dynamics is asymptotically mean square admissible and has a prescribed H_∞ performance for a class of singular stochastic nonlinear systems is proposed. Furthermore, a sliding mode control law is synthesized such that the singular stochastic nonlinear system can be driven to the sliding surface in finite time. Finally, a numerical example is proposed to illustrate the effectiveness of the given theoretical results.     

一类基于观测器的非线性网络化控制系统的绝对稳定性

主要考虑了基于观测器的Lurie网络化控制系统的绝对稳定性问题. 由于采用了基于观测器的反馈控制器, 传感器到控制器的网络诱导时延和控制器到执行器的网络诱导时延不再能合并到一起处理. 首先通过状态增广方法将Lurie网络化控制系统建模为一个多时滞的Lurie系统, 然后利用Newton-Leibniz公式和添加自由权矩阵的方法给出了时滞依赖的稳定性条件. 在此基础上, 给出三种求解控制器和观测器增益矩阵的方法. 此外, 还分别给出了被控对象存在范数有界不确定性和结构不确定性时系统的鲁棒稳定性条件及鲁棒控制器设计方法, 所有得到的结果都是以线性矩阵不等式的形式给出的. 便于利用线性矩阵不等式工具包进行求解. 最后, 通过两个仿真算例说明了方法的可行性和有效性.     

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。     

Event-triggered sliding mode control for a class of nonlinear systems

ABSTRACT

Event-triggering strategy is one of the real-time control implementation techniques which aims at achieving minimum resource utilisation while ensuring the satisfactory performance of the closed-loop system. In this paper, we address the problem of robust stabilisation for a class of nonlinear systems subject to external disturbances using sliding mode control (SMC) by event-triggering scheme. An event-triggering scheme is developed for SMC to ensure the sliding trajectory remains confined in the vicinity of sliding manifold. The event-triggered SMC brings the sliding mode in the system and thus the steady-state trajectories of the system also remain bounded within a predesigned region in the presence of disturbances. The design of event parameters is also given considering the practical constraints on control execution. We show that the next triggering instant is larger than its immediate past triggering instant by a given positive constant. The analysis is also presented with taking delay into account in the control updates. An upper bound for delay is calculated to ensure stability of the system. It is shown that with delay steady-state bound of the system is increased than that of the case without delay. However, the system trajectories remain bounded in the case of delay, so stability is ensured. The performance of this event-triggered SMC is demonstrated through a numerical simulation.     

Observer-based sliding mode control of Markov jump systems with random sensor delays and partly unknown transition rates

In this paper, the sliding mode control problem of Markov jump systems (MJSs) with unmeasured state, partly unknown transition rates and random sensor delays is probed. In the practical engineering control, the exact information of transition rates is hard to obtain and the measurement channel is supposed to subject to random sensor delay. Design a Luenberger observer to estimate the unmeasured system state, and an integral sliding mode surface is constructed to ensure the exponential stability of MJSs. A sliding mode controller based on estimator is proposed to drive the system state onto the sliding mode surface and render the sliding mode dynamics exponentially mean-square stable with H_∞ performance index. Finally, simulation results are provided to illustrate the effectiveness of the proposed results.     

Lurie 型直接控制系统的绝对稳定性

Lurie型控制系统是一类非常典型的非线性控制系统,具有广泛的实际工程应用背景.本文利用Popov频域法,研究了一类Lurie型直接控制系统的绝对稳定性.在系统矩阵无对角线相等情形假设的一般条件下,给出了该类系统绝对稳定的一些充分必要条件.这些结论推广了前人所取得的研究成果.     

Absolute stability and stabilization for Lurie networked control systems

This paper investigates the problem of absolute stability and stabilization for networked control systems (NCSs) with the controlled plant being Lurie systems (Lurie NCSs), in which the network‐induced delays are assumed to be time‐varying and bounded. By considering the relationship between the network‐induced delay and its upper bound, an improved stability criterion for networked control system is proposed. Furthermore, the resulting condition is extended to design a state feedback controller by employing an improved cone complementary linearization (ICCL) algorithm. A numerical example is worked out to illustrate the effectiveness and the benefits of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd.     

LMI approach for absolute stability of general neutral type Lurie indirect control systems

This paper deals with the problem of the absolute stability for general neutral type Lurie indirect control systems by Lyapunov method and linear matrix inequality (LMI) technique. Delay_dependent sufficient conditions for the absolute stability are derived and expressed as the feasibility problem of LMI, which can be easily solved by Matlab Toolbox. Finally, some examples are provide to demonstrate the effectiveness of proposed method.     

LMI approach for absolute stability of general neutral type Lurie indirect control systems

This paper deals with the problem of the absolute stability for general neutral type Lurie indirect control systems by Lyapunov method and linear matrix inequality （LMI） technique. Delay-dependent sufficient conditions for the absolute stability are derived and expressed as the feasibility problem of LMI, which can be easily solved by Matlab Toolbox. Finally, some examples are provide to demonstrate the effectiveness of proposed method.     

具有多个非线性项的一般Lurie间接系统的绝对稳定性

为了研究具有多个非线性项的一般Lurie间接系统的绝对稳定性问题,介绍了关于变 元σ绝对稳定的概念.通过对关于变元σ绝对稳定性的研究,得到了此类系统绝对稳定的充要 条件,并给出了一些简洁实用的充分条件.     

时变时滞Lurie控制系统的绝对稳定性

基于Lyapunov稳定性定理,利用线性矩阵不等式方法给出了系统绝对稳定的判别准则.讨论了具有多个时变时滞的Lurie直接控制系统和Lurie间接控制系统的绝对稳定性.所得结论是时滞无关的,即绝对稳定性充分条件仅依赖于时滞导数的大小,特别地,时滞可为无界函数.通过一个示例说明有时得到时滞相关的绝对稳定性条件比时滞无关的稳定性条件具有更大的保守性,促使今后寻找另外的方法和工具得到保守性较低的稳定性条件.仿真示例同时说明此方法对时滞为无界函数时的有效性.     

具有时滞的Lurie型控制系统绝对稳定的时滞相关准则

研究了具有时滞的Lurie型控制系统的绝对稳定性,利用矩阵不等式的方法出了系统绝对稳定的时滞相关准则,与现有的结果相比,具有较小的保守性。     

Design of adaptive block backstepping controllers for uncertain nonlinear dynamic systems with n blocks

Based on the Lyapunov stability theorem, a design methodology of adaptive block backstepping control is proposed in this article for a class of multi-input systems with matched and mismatched perturbations to solve regulation problems. The systems to be controlled contain n blocks' dynamic equations, hence n???1 virtual input controllers are firstly designed so that the state variables of first n???1 blocks are asymptotically stable if each virtual control input is equal to the state variable of next block. Then the control input is designed in the last nth block to ensure asymptotic stability for the whole state variables even if the perturbations exist. In addition, adaptive mechanisms are embedded in each virtual input function and control input, so that the upper bound of perturbations is not required to be known beforehand. Finally, a numerical example is given for demonstrating the feasibility of the proposed control scheme.