具有结构不确定性的输出反馈线性系统的鲁棒稳定性分析

基于向量的幂变换方法，对具有结构不确定性的输出反馈线性系统的鲁棒稳定性问题作了分析。单参数摄动时给出了闭环系统鲁棒稳定的充要条件，多参数摄动时得到了保证系统鲁棒稳定的充分条件，导出了闭环系统鲁棒稳定区域的一种代数表达形式。最后给出了实例。     

具有结构不确定性的输出反馈性系统的鲁棒稳定性分析

基于向量的幂变换方法，对具有结构不确定性的输出反馈线性系统的鲁棒稳定性问题作了分析。单参数摄动时给出了闭环系统鲁棒稳定的充要条件，多参数摄动时得到了保证系统鲁棒稳定的充分条件，导出了闭环系统鲁棒稳定区域的一种代数表达形式。最后给出了实例。     

SISO动态矩阵控制的鲁棒稳定性条件

定量分析了单输入单输出(SISO)动态矩阵控制系统的鲁棒稳定条件,采用脉冲响应模型簇来描述被控过程的不确定性,并讨论了基于脉冲响应模型(FIR)的动态矩阵控制(DMC)算法;在此基础上,推导了DMC闭环系统的鲁棒稳定条件.     

非最小相位不稳定对象的鲁棒最优模型匹配

研究了单输入单输出(SISO)线性时不变系统的鲁棒最优模型匹配问题.采用二自由度的控制器,对于被控对象具有乘性摄动时,充分考虑控制器的自由参数,将问题转化成有约束的H∞控制问题,使闭环系统既是H∞范数意义下的最优模型匹配,又具有更大的鲁棒稳定性.最后,通过解两个H∞范数的最优内插问题,给出了一种新的设汁方法来确定控制器的参数.该方法简单、直接,对非最小相位系统和不稳定系统均适用.     

鲁棒稳定性和鲁棒对角优势的关系

本文研究了多输入多输出系统的鲁棒稳定性和鲁棒对角优势的关系.不仅给出了使系统 鲁棒对角优势所需的鲁棒稳定性条件,而且还得出了系统鲁棒对角优势一定保证系统鲁棒稳 定这个一般性的结论.并可根据本文所给的结果,对允许摄动的最大边界进行估计,包括非结 构摄动的范数上界和结构性摄动的摄动矩阵的各元素的模的估计.本文得出的鲁棒对角优势 保证鲁棒稳定的结果是较少保守性的.     

具有扰动输入的不确定性非线性系统的输出调节极限性能

本文研究了一类具有扰动输入的不确定性非线性系统的输出调节问题, 给出了该类系统在最差的不确定性参数和扰动输入情况下系统输出调节的极限性能. 所讨论的非线性系统是可镇定非最小相位系统, 并且该系统的零动态由“鲁棒输入对状态稳定(robust input-to-state stable)部分”和“不稳定但可镇定部分”组成. 假设系统的不确定性参数和扰动输入分别以非线性函数和仿射形式同时出现在系统零动态的鲁棒输入对状态稳定部分和系统的可线性化部分, 而且其可线性化部分的不确定性具有下三角形结构形式. 该系统输出调节问题的性能以其输出信号能量作为度量. 对于上述非线性系统, 在最差的不确定性参数和扰动输入情况下, 输出调节问题的极限性能只取决于镇定其零动态“不稳定部分”所需的最小能量.     

基于DCS的预测PID控制系统鲁棒稳定性分析

针对基于DCS的预测PID的控制系统.利用Kharitonov定理和边缘理论分析其在参数不确定情况下输入、输出的鲁棒稳定性.具体就SOPDT(二阶加纯滞后)对象给出了系统保持稳定的最大过程参数区间,并对非最小相位系统进行了简单分析.理论分析和仿真结果表明,当过程参数偏离标称值时,该算法能使系统保持很好的鲁棒稳定性.     

参数摄动混杂离散系统的鲁棒稳定性

采用线性矩阵不等式(LMI)方法研究离散事件状态转移条件为状态依赖的参数摄动线性混杂离散系统的鲁棒稳定性问题, 提出此类系统全局鲁棒渐近稳定性判定定理, 基于分段Lyapunov函数给出了一般混杂离散系统在Lyapunov意义下局部稳定的判定定理, 该定理可将线性混杂离散系统的稳定性问题转化为LMI问题, 在此基础上提出了参数摄动线性混杂离散系统在Lyapunov意义下局部鲁棒稳定的充分条件.     

离散非线性系统的迭代学习轨迹跟踪鲁棒算法优化及应用

针对一类存在随机输入状态扰动、输出扰动及系统初值与给定期望值不严格一致的离散非线性重复系统,提出了一种P型开闭环鲁棒迭代学习轨迹跟踪控制算法．基于λ范数理论证明了算法的严格鲁棒稳定性,并通过多目标函数性能指标优化P型开闭环迭代学习控制律的增益矩阵参数,保证了优化算法下系统输出期望轨迹跟踪误差的单调收敛性,达到提高学习算法收敛速度和跟踪精度的目的．最后应用于二维运动移动机器人的实例仿真,验证了本文算法的可行性和有效性．     

多变量网络化DMC算法的鲁棒稳定性研究

在工业控制系统优化算法的研究中,引入网络化控制系统,针对多输入多输出动态矩阵控制(DMC)算法的鲁棒稳定性问题,首先根据有限脉冲响应(FIR)模型导出了网络控制系统通信信道上存在随机网络诱导时延的网络化DMC算法;其次,在考虑预测模型与系统实际模型之间存在模型失配情况下,利用线性矩阵不等式方法(LMI)分析该网络化DMC算法的鲁棒稳定性问题,进而建立了网络化DMC算法的鲁棒稳定性的充分条件。数值仿真验证表明解决工业控制系统性能优化的有效性。     

Robust stability and H-infinity control for uncertain discrete-time Markovian jump singular systems

The robust stability and stabilization, and H-infinity control problems for discrete-time Markovian jump singular systems with parameter uncertainties are discussed. Based on the restricted system equivalent (r.s.e.) transformation and by introducing new state vectors, the singular system is transformed into a discrete-time Markovian jump standard linear system, and the linear matrix inequality (LMI) conditions for the discrete-time Markovian jump singular systems to be regular, causal, stochastically stable, and stochastically stable with °- disturbance attenuation are obtained, respectively. With these conditions, the robust state feedback stochastic stabilization problem and H-infinity control problem are solved, and the LMI conditions are obtained. A numerical example illustrates the effectiveness of the method given in the paper.     

A robust stabilization problem of fuzzy control systems and itsapplication to backing up control of a truck-trailer

A robust stabilization problem for fuzzy systems is discussed in accordance with the definition of stability in the sense of Lyapunov. We consider two design problems: nonrobust controller design and robust controller design. The former is a design problem for fuzzy systems with no premise parameter uncertainty. The latter is a design problem for fuzzy systems with premise parameter uncertainty. To realize two design problems, we derive four stability conditions from a basic stability condition proposed by Tanaka and Sugeno: nonrobust condition, weak nonrobust condition, robust condition, and weak robust condition. We introduce concept of robust stability for fuzzy control systems with premise parameter uncertainty from the weak robust condition. To introduce robust stability, admissible region and variation region, which correspond to stability margin in the ordinary control theory, are defined. Furthermore, we develop a control system for backing up a computer simulated truck-trailer which is nonlinear and unstable. By approximating the truck-trailer by a fuzzy system with premise parameter uncertainty and by using concept of robust stability, we design a fuzzy controller which guarantees stability of the control system under a condition. The simulation results show that the designed fuzzy controller smoothly achieves backing up control of the truck-trailer from all initial positions     

Delay‐dependent robust stability for stochastic time‐delay systems with polytopic uncertainties

This paper considers a delay‐dependent and parameter‐dependent robust stability criterion for stochastic time‐delay systems with polytopic uncertainties. The delay‐dependent robust stability criterion, as expressed in terms of linear matrix inequalities (LMIs), is obtained by using parameter‐dependent Lyapunov functions. It is shown that the result derived by a parameter‐dependent Lyapunov functional is less conservative. Numerical examples are provided to illustrate the effectiveness of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd.     

Robust stability under structured and unstructured perturbations

The problem of robust stability for linear time-invariant single-output control systems subject to both structured (parametric) and unstructured (H_∞) perturbations is studied. A generalization of the small gain theorem which yields necessary and sufficient conditions for robust stability of a linear time-invariant dynamic system under perturbations of mixed type is presented. The solution involves calculating the H_∞ -norm of a finite number of extremal plants. The problem of calculating the exact structured and unstructured stability margins is then constructively solved. A feedback control system containing a linear time-invariant plant which is subject to both structured and unstructured perturbations is considered. The case where the system to be controlled is interval is treated, and a nonconservative, easily verifiable necessary and sufficient condition for robust stability is given. The solution is based on the extremal of a finite number of line segments in the plant parameter property of a finite number of line segments in the plant parameter space along which the points closest to instability are encountered     

Robust H∞ control for uncertain discrete‐time stochastic bilinear systems with Markovian switching

This paper is concerned with the problems of robust stochastic stabilization and robust H_∞ control for uncertain discrete‐time stochastic bilinear systems with Markovian switching. The parameter uncertainties are time‐varying norm‐bounded. For the robust stochastic stabilization problem, the purpose is the design of a state feedback controller which ensures the robust stochastic stability of the closed‐loop system irrespective of all admissible parameter uncertainties; while for the robust H_∞ control problem, in addition to the robust stochastic stability requirement, a prescribed level of disturbance attenuation is required to be achieved. Sufficient conditions for the solvability of these problems are obtained in terms of linear matrix inequalities (LMIs). When these LMIs are feasible, explicit expressions of the desired state feedback controllers are also given. An illustrative example is provided to show the effectiveness of the proposed approach. Copyright © 2005 John Wiley & Sons, Ltd.     

Further remarks on asymptotic stability and set invariance for linear delay-difference equations

We studied the existence of positively invariant sets for linear delay-difference equations. In particular, we regarded two strong stability notions: robust (with respect to delay parameter) asymptotic stability for the discrete-time case and delay-independent stability for the continuous-time case. The correlation between these stability concepts is also considered. Furthermore, for the delay-difference equations with two delay parameters, we provided a computationally efficient numerical routine which is necessary to guarantee the existence of contractive sets of Lyapunov–Razumikhin type. This condition also appears to be necessary and sufficient for the delay-independent stability and sufficient for the robust asymptotic stability.     

Depth control of autonomous underwater vehicles using indirect robust control method

In this article, we propose a robust depth control design scheme for autonomous underwater vehicles (AUVs) in the presence of hydrodynamic parameter uncertainties and disturbances. The controller is designed via a new indirect robust control method that handles the uncertainties by formulating the uncertainty bounds into the cost functional and then transforming the robust control problem into an equivalent optimal control problem. Both robust asymptotic stability and optimality can be achieved and proved with this new formulation. The θ-D method is utilised to solve the resultant nonlinear optimal control problem such that an approximate closed-form feedback controller can be obtained and thus is easy to implement onboard without intensive computation load. Simulation results demonstrate that robust depth control is accomplished under the system parameter uncertainties and disturbances with small control fin deflection requirement.     

Systems with structured uncertainty: relations between quadraticand robust stability

The relation between the notions of robust stability and quadratic stability for uncertain systems with structured uncertainty due to both real and complex parameter variations is discussed. Examples are presented to demonstrate that for systems containing at least two uncertain blocks, the notions of robust stability for complex parameter variations and quadratic stability for real parameter variations are not equivalent. A byproduct of these examples is that, for this class of systems, quadratic stability for real perturbations need not imply quadratic stability for complex perturbations. This is in stark contrast with the situation in the case of unstructured uncertainty, for which it is known that quadratic stability for either real or complex perturbations is equivalent to robust stability for complex perturbations, and thus equivalent to a small gain condition on the transfer matrix that the perturbation experiences