Robust pole assignment in systems subject to structured perturbations

The problem of robust pole assignment by feedback in a linear, multivariable, time-invariant system which is subject to structured perturbations is investigated. A measure of robustness, or sensitivity, of the poles to a given class of perturbations is derived, and a reliable and efficient computational algorithm is presented for constructing a feedback which assigns the prescribed poles and optimizes the robustness measure.     

Necessary and sufficient stability condition of fractional-order interval linear systems

This paper establishes a necessary and sufficient stability condition of fractional-order interval linear systems. It is supposed that the system matrix A is an interval uncertain matrix and fractional commensurate order belongs to 1≤α<2. Using the existence condition of Hermitian P=P^∗ for a complex Lyapunov inequality, we prove that the fractional-order interval linear system is robust stable if and only if there exists Hermitian matrix P=P^∗ such that a certain type of complex Lyapunov inequality is satisfied for all vertex matrices. The results are directly extended to the robust stability condition of fractional-order interval polynomial systems.     

Continuous pole placement for delay equations

In this paper, we describe a stabilization method for linear time-delay systems which extends the classical pole placement method for ordinary differential equations. Unlike methods based on finite spectrum assignment, our method does not render the closed loop system, finite dimensional but consists of controlling the rightmost eigenvalues. Because these are moved to the left half plane in a (quasi-)continuous way, we refer to our method as continuous pole placement. We explain the method by means of the stabilization of a linear finite dimensional system in the presence of an input delay and illustrate its applicability to more general stabilization problems.     

Dominant pole and eigenstructure assignment for positive systems with state feedback

In this paper, the dominant pole assignment problem, the dominant eigenstructure assignment problem and the robust dominant pole assignment problem for linear time-invariant positive systems with state feedback are considered. The dominant pole assignment problem is formulated as a linear programming problem, and the dominant eigenstructure problem is formulated as a quasiconvex optimisation problem with linear constraints. The robust dominant pole assignment problem is formulated as a non-convex optimisation problem with non-linear constraints which is solved using particle swarm optimisation (PSO) with an efficient scheme which employs the dominant eigenstructure assignment technique to accelerate the convergence of the PSO procedure. Each of the three problems can be further constrained by requiring that the controller has a pre-specified structure, or the gain matrix have both elementwise upper and lower bounds. These constraints can be incorporated into the proposed scheme without increasing the complexity of the algorithms. Both the continuous-time case and the discrete-time case are treated in the paper.     

极点位于指定区域的不确定参数边界

本文研究了极点位于指定区域的不确定参数边界估计问题。该问题包括了两个子问题－极点的鲁棒性分析和配置极点于任意指定区域的控制器参数化，基于广义Ｌｙａｐｕｎｏｖ理论和特征值分解，提出了一种解决该问题的新方法。得到的边界不必为对称的，许多现有的不确定参数边界均包含在边界中。     

Necessary and sufficient ergodicity condition for open synchronizedqueueing networks

A necessary and sufficient ergodicity condition for complex open queueing systems is given. The queueing networks considered belong to a particular class of unbounded Markov stochastic Petri nets. These systems can include synchronization features like fork and join arrivals and departures, and feedback between behavior of different queues. Grouped and correlated arrivals and departures are also allowed. An example and a proof of the ergodicity results are presented     

图同构的一个充分必要条件

图同构的判定性问题是图论理论中的一个难问题,至今没有得到彻底解决。Ulam曾经提出过一个判定图同构的猜想,也称为图的重构猜想。提出了一个新的判定图同构的充分必要条件,即在子图同构的前提下,根据新增顶点及相应关联边的关系,判断母图同构的充分必要条件。基于具有同构关系的对应点无限衍生技术,采用数学归纳法证明了这个充分必要条件的成立。     

极点配置问题线性可解的充要条件

本文研究线性系统在输出反馈作用下的极点配置问题,得到了系统可由"线性化"方法任意配置n个(等于系统的维数)闭环极点的充要条件.并给出了一种新的极点配置方法.     

Robust pole assignment for incomplete nonlinear decoupling applied to robots

A robustness analysis and synthesis for incomplete nonlinear decoupling for a class of nonlinear systems is discussed. Rigid and elastic-joint robot models belong to this class. For the elastic case, a transformation facilitates the robustness analysis under a weak assumption. Charts with H ₁- and H - norms of closed-loop disturbance transfer functions of the nonlinear-decoupled system are presented for a robust pole assignment.     

Almost disturbance decoupling and pole placement

We revisit here the Almost Disturbance Decoupling Problem (ADDP) (Willems, 1981) by state feedback with the objective to solve ADDP and simultaneously place the maximal number of poles in the closed-loop solution. Indeed, when ADDP is solvable, we show that, whatever be the choice of a particular feedback solution, the obtained closed-loop system always has a set of fixed poles. We characterize these Fixed Poles of ADDP. The other (non-fixed) poles can be placed freely, and we characterize the “optimal” solutions (in terms of ad hoc subspaces and feedbacks) which allow us to solve ADDP with maximal pole placement. From our contribution, which treats the most general case for studying ADDP with maximal, usually partial, pole placement, directly follow the solutions of ADDP with complete pole placement (when there are no ADDP Fixed Poles) and ADDP with internal stability (when all the Fixed Poles of ADDP are stable), without requiring the use of stabilizability subspaces, as in Willems (1981). We extend the concept of Self-Bounded Controlled-Invariant Subspaces (Basile & Marro, 1992) to almost ones. An example is proposed that illustrates our contributions.     

线性离散系统具有闭环极点约束的输出反馈H∞ 控制

对一类线性离散系统, 研究了具有闭环圆盘极点约束的输出反馈H_∞ 控制问题. 基于线性矩阵不等式处理方法, 导出了输出反馈控制器的存在条件和设计方法. 和现有方法相比, 本文的方法具有更小的保守性.     

Necessary and sufficient condition for convergence of iterative learning algorithm

This correspondence is concerned with an iterative learning algorithm for MIMO linear time-varying systems. We provide a necessary and sufficient condition for the existence of a convergent algorithm. The result extends the main result in Saab (IEEE Trans. Automat. Control 40(6) (1995) 1138).     

区间矩阵二次稳定的充分必要条件

提出了区间矩阵二次稳定的充分必要条件,以及相应的稳定裕度的计算方法.结论以线性矩阵不等式(LMI)的形式给出.利用功能强大的LMI工具,求解非常方便.所给实例表明,该方法用于确定区间矩阵的鲁棒稳定性及其稳定裕度,非常有效.     

Necessary and sufficient condition for the existence of Kharitonov-like theorems

Kharitonov has shown that a family of interval polynomials is Hurwitz if and only if the vertex polynomials are Hurwitz. A necessary and sufficient condition to check the existence of Kharitonov-like theorems for other regions of interest in the complex plane is presented.     

基于极点配置的平整机张力解耦控制

分析了平整机产品质量存在的问题 ;提出了基于极点配置的解耦控制策略. 理论分析、计算机仿真和工业实验都表明该控制方法能实现对平整机前张力、后张力和工作辊速度的解耦控制, 降低了它们之间的相互耦合程度, 改善了系统的控制效果, 有利于提高带材产品的质量.     

Regional pole assignment for uncertain delta-operator systems

The pole assignment in a specified disk by state feedback for uncertain delta-operator systems is studied. By making use of algebra Riccati equations, a sufficient and necessary condition of pole assignment for a kind of parameter uncertain delta-operator system in a specified disk by state feedback is presented. And the design method of state feedback controller is also developed.The proposed method can unify some previous rehted results of continuous and discrete time systems into the delta framework. The efficiency of the design method is illustrated by a numerical example.     

Necessary and sufficient condition for stability robustness under known additive perturbation

A necessary and sufficient condition is derived for the stability robustness of a unity feedback closed-loop system involving a strictly proper plant P₀ and a stabilizing compensator C₀ under the assumption that the plant P₀ is perturbed to P₀ + ΔP₀ where ΔP₀ is a known strictly proper rational matrix.     

Augmented gradient flows for on-line robust pole assignment via state and output feedback

This paper is concerned with robust pole assignment in synthesis of linear control systems via state and output feedbacks. First, both the pole assignment and robustness requirements are appropriately formulated as two optimization problems. Then, gradient flow models are developed for the on-line computation of feedback gain matrices that result in robust pole assignment by solving these two optimization problems. A technique is introduced to facilitate the real-time matrix inverse involved for realizing the gradient flow models. The resulting augmented gradient flows have desired convergence properties. Simulation results are included to show the effectiveness of the proposed approach.     

A necessary condition for pole assignment by constant output feedback

In this paper we shall investigate the pole assignment problem by constant output feedback using transfer function techniques. In particular, a necessary condition is given for the existence of constant output feedback which assigns the eigenvalues of closed-loop system to any desired positions.     

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.