线性离散不确定系统区域极点配置的状态反馈实现方法

研究利用状态反馈对线性离散不确定系统进行区域极点配置的问题。导出了一个由离散代数Ｒｉｃａｔｉ方程表示的对线性离散不确定系统进行区域极点配置的充分条件,并给出了一个通过求解该方程来确定状态反馈增益矩阵的算法。     

不确定广义系统的圆形区域极点配置

考虑不确定连续或离散广义系统的圆形区域极点配置问题, 目的是设计状态反 馈控制律, 使得闭环系统正则, 无脉冲(连续广义系统情形)或因果(离散广义系统情形), 且 闭环极点位于一给定的圆形区域内. 给出了所期望的状态反馈控制律存在的充分条件及其解 析表达式.     

A note on pole assignment in uncertain systems

A new method for full-rank state-feedback pole assignment is introduced. A particular advantage of this method is that no freedom in the design parameters is lost. Hence, further design problems such as robust pole assignment in uncertain systems are alleviated. An application of this feature is shown for a particular linear model of the F16 aircraft. The connections between state feedback and several concepts in the literature such as incomplete input feedback, incomplete state feedback, output feedback and incomplete pole assignment are also given.     

Pole assignment in a specified disk

The problem of assigning all poles of a closed-loop system in a specified disk by state feedback is considered for both continuous and discrete systems. A state feedback control law is determined by using a discrete Riccati equation. This kind of pole assignment problem is namedD-pole assignment, and its relation to the optimal control problem and its robustness properties are discussed. The gain and phase margins for all closed-loop poles to stay inside the specified diskDare determined for the proposed control.     

一类连续区间系统的鲁棒圆盘极点配置

针对一类连续线性区间系统,基于线性矩阵不等式,介绍一类能够将给出的连续区间系统的闭环系统的极点配置到指定圆盘中的状态反馈和输出反馈增益矩阵的设计方法.这类设计方法也包括分别基于执行器故障和传感器故障的可靠控制器的设计方法,基于矩阵的谱半径不大于自身的最大奇异值的理论以及矩阵的Schur补引理,将矩阵的最大奇异值限定后就...     

Pole assignment for uncertain systems in a specified disk by statefeedback

This paper presents a method for assigning the poles in a specified disk by state feedback for a linear discrete or continuous time uncertain system, the uncertainty being norm bounded. For this the “quadratic d stabilizability” concept which is the counterpart of quadratic stabilizability in the context of pole placement is defined and a necessary and sufficient condition for quadratic d stabilizability derived. This condition expressed as a parameter dependent discrete Riccati equation enables one to design the control gain matrix by solving iteratively a discrete Riccati equation     

Pole assignment for uncertain systems in a specified disk by output feedback

In this paper the problem of pole assignment in a disk by output feedback for continuous-or discrete-time uncertain systems is addressed. A necessary and sufficient condition for quadratic d stabilizability by output feedback is presented. This condition is expressed in terms of two parameter-dependent Riccati equations whose solutions satisfy two extra conditions. An output d stabilization algorithm is derived and a controller formula given.     

Output feedback disk pole assignment for systems with positive realuncertainty

In this paper, the problem of pole assignment in a disk by output feedback for continuous or discrete-time uncertain systems is addressed. A necessary and sufficient condition for quadratic d stabilizability by output feedback is presented. This condition is expressed in terms of two parameter-dependent Riccati equations whose solutions satisfy two extra conditions. An output d stabilization algorithm is derived and a controller formula given. Some related problems are also discussed     

区域极点约束下线性离散系统的Riccati鲁棒控制

讨论区域极点约束下,含结构参数扰动的不确定线性离散系统的鲁棒控制问题,即设计一 鲁棒状态反馈控制器,使线性离散系统在可允许的参数扰动下,闭环矩阵极点始终位于一预先 给定的圆形区域中,从而闭环系统具有期望的动态性能.上述控制目的可通过求解一含参数 的代数离散Riccati方程达到.     

具有传感器故障的可靠圆盘极点配置

针对线性定常系统，提出了考虑传感器故障的指定圆盘极点配置可靠控制问题，在考虑更一般、更实际的传感器故障模型的基础上，给出了系统将极点配置到指定圆盘内的充分条件，通过求解LMI完成状态反馈控制器的设计，仿真例子验证了该结果的可行性，并进一步说明了对系统进行可靠设计的必要性。     

Pole assignment in a specified circular region using a bilinear transformation onto the unit circle

An algorithm for pole assignment in a specified circular region using a bilinear transformation onto the unit circle is considered, A Lyapunov type test is developed to check that all the eigenvalues of a discrete system are within a circle in the complex plane. Pole placement in a circular region by LQ state feedback design is investigated for discrete linear systems. Perturbation bounds are derived, using bilinear transformation, for all closed-loop poles of a perturbed discrete system to remain inside a specified circular region. Illustrative examples are included     

不确定离散广义系统的D稳定鲁棒控制

研究了具有圆盘区域极点约束的一类不确定离散广义系统的鲁棒控制问题.首先,研 究了控制输入项不含扰动的不确定离散广义系统,提出了广义二次D镇定的概念,基于矩阵不 等式和广义Riccati方程,给出了一种广义二次D镇定器的设计方法,所得到的结论能够实现研 究目标;然后,讨论了控制输入项含有扰动的不确定离散广义系统,在一定的假设条件下,给出 了期望状态反馈增益阵的存在条件及其解析表达式.最后,用数值示例说明所给方法的有效性 及可行性.     

不确定系统D稳定与方差约束的鲁棒H∞可靠控制

研究了一类不确定系统区域稳定和方差约束的鲁棒H∞可靠控制器的设计方法,其目的是通过设计状态反馈控制器,使闭环系统的极点被配置在给定的圆盘中,同时,当有外生扰动,以及所有可能的不确定及其敏感执行器失效的时候,依然能满足闭环传递函数H∞范数有界和稳态方差的约束.借助于LMI和凸优化技术,给出了控制器存在的充分条件及其解析式.最后,通过一个仿真例子,说明该方法的可行性.     

A Lyapunov approach to analysis of discrete singular systems

In this paper, a new type generalized Lyapunov equation for discrete singular systems is proposed. Then it is applied to study problems such as pole clustering, controllability and observability for discrete singular systems. First, some necessary and sufficient conditions for pole clustering are derived via the solution of this new type Lyapunov equation. Further, the relationship between the solution of the Lyapunov equation and structure properties of discrete singular systems will be investigated based on these results. Finally, a type of generalized Riccati equation is proposed and its solution is used to design state feedback law for discrete singular systems such that all the finite poles of the closed-loop systems are clustered into a specified disk.     

圆盘区域极点约束鲁棒非脆弱控制

针对一类参数不确定线性系统,研究了具有圆盘区域极点约束的状态反馈鲁棒非脆弱控制器设计问题.系统中的参数不确定性满足范数有界条件,设计的非脆弱控制器具有加性和乘性不确定项.基于线性矩阵不等式(LMI),提出了将闭环系统极点配置到指定圆盘区域的状态反馈鲁棒非脆弱控制器存在的充分条件.然后利用G辅助变量替换技术拓展了圆盘极点配置的线性矩阵不等式(LMI)条件,提出保守度较低的状态反馈非脆弱控制器设计方法.数值仿真例子验证了给出的控制器设计方法的可行性.     

A gradient flow approach to on-line robust pole assignment for synthesizing output feedback control systems

Pole assignment is a basic design method for synthesis of feedback control systems. In this paper, a gradient flow approach is presented for robust pole assignment in synthesizing output feedback control systems. The proposed approach is shown to be capable of synthesizing linear output feedback control systems via on-line robust pole assignment. Convergence of the gradient flow can be guaranteed. Moreover, with appropriate design parameters the gradient flow converges exponentially to an optimal solution to the robust pole assignment problem and the closed-loop control system based on the gradient flow is globally exponentially stable. These desired properties make it possible to apply the proposed approach to slowly time-varying linear control systems. Simulation results are shown to demonstrate the effectiveness and advantages of the proposed approach.     

具有分布时滞不确定系统的滑模控制

针对一类含有分布时滞的不确定系统,通过利用Lyapunov稳定性理论和线性矩阵不等式方法进行滑模控制研究.首先,构造滑模控制器,使得系统满足滑模到达条件;其次,通过构造适当的Lyapunov泛函,给出闭环系统渐近稳定的充分条件.该充分条件通过采用虚拟反馈控制思想,结合状态反馈的极点配置方法,转换为线性矩阵不等式的形式,...     

线性不确定系统混合故障的可靠圆盘极点配置

针对一类不确定线性系统,利用更一般、更实际的执行器出现混合故障的模型,设计可靠控制器的同时将系统的极点配置到指定圆盘内问题,混合故障模型是指在一个系统中同时包含离散故障模型和连续故障模型,并给出系统将极点配置到指定圆盘上可靠控制的充分条件.通过求解LMI(线性矩阵不等式)完成状态反馈可靠控制器的设计.仿真验证本文提出的...     

广义系统极点配置的一种代数几何方法

利用代数几何方法给出了可任意配置极点的条件，并证明了实数域上广义系统若存在复反馈配置极点，则一定存在实反馈配置极点．     

广义系统极点配置的一种代数几何方法

利用代数几何方法给出了可任意配置极点的条件,并证明了实数域上广义系统若存在复 反馈配置极点,则一定存在实反馈配置极点.