Two parametric approaches for eigenstructure assignment in second-order linear systems

This paper considers eigenstructure assignment in second-order linear systems via proportional plus derivative feedback. It is shown that the problem is closely related to a type of so-called second-order Sylvester matrix equations. Through establishing two general parametric solutions to this type of matrix equations, two complete parametric methods for the proposed eigenstructure assignment problem are presented. Both methods give simple complete parametric expressions for the feedback gains and the closed-loop eigenvector matrices. The first one mainly depends on a series of singular value decompositions, and is thus numerically simple and reliable; the second one utilizes the right factorization of the system, and allows the closed-loop eigenvalues to be set undetermined and sought via certain optimization procedures. An example shows the effectiveness of the proposed approaches. Keywords Second-order linear systems - Eigenstructure assignment - Proportional plus derivative feedback - Parametric solution - Singular value decompoition - Right factorization This work was supported in part by the Chinese Outstanding Youth Foundation (No.69504002).

Duality of 2-D singular systems of Roesser models

In this paper, the properties and concepts of dual systems of the two-dimensional singular Roesser models （2-D SRM） are studied. Two different concepts of the dual systems are proposed for the 2-D SRM. One is derived from the duality defined for two-dimensional singular general models （2-D SGM）-called the S-dual systems; the other one is defined based on 2-D SRM in a traditional sense-called the T-dual systems. It is shown that if a 2-D SRM is jump-mode free or jump-mode reachable, then it can be equivalently transformed into a canonical form of a 2-D SRM, for which the T-duality and the S-duality are equivalent. This will be of some perspective applications in the robust control of 2-D SRM.

Conditions for Robust D-Stability of Discrete-Delay Perturbed Singular Systems

In this paper, a sufficient condition of robust D-stability for discrete-delay perturbed singular systems is presented, and the robust stability sufficient condition is independent of the delay. Two classes of perturbations for systems are discussed: (1) highly structured parametric perturbations; (2) unstructured parametric perturbations. An useful technique for robust pole-assignment in a specified circular region is also proposed, the criterion is tested easily, and convenient for the application in the engineering. Two examples have been given to validate the proposed method.

Robust D stabilization of singular systems with polytopic uncertainties

The robust D stabilization problem is considered for singular systems with polytopic uncertainties in this paper.Both the derivative matrix E and the state matrix A are with uncertainties,which were not considered before.First,with the introduction of some free matrices,a necessary and sufficient condition for the singular system to be D stable is proposed,based on which,the robust D stable problem is solved,and a sufficient condition for the closed system to be robust D stabilizable is obtained.The desired state feedback controller is given in an explicit expression.Numerical examples show the efficiency of the proposed approach.

Eigenstructure assignment in a class of second-order dynamic systems

Eigenstructure assignment using the proportional-plus-derivative feedback controller in a class of secondorder dynamic system is investigated. Simple, general, complete parametric expressions for both the closed-loop eigenvector matrix and the feedback gains are established based on two simple Smith form reductions. The approach utilizes directly the original system data and involves manipulations only on n-dimensional matrices. Furthermore, it reveals all the degrees of freedom which can be further utilized to achieve additional system specifications. An example shows the effect of the proposed approach.

Eigenstructure Assignment in a Class of Second-order Descriptor Linear Systems: A Complete Parametric Approach

In this paper eigenstructure assignment via proportional-plus-derivative feedback is investigated for a class of second-order descriptor linear systems. Under certain conditions, simple, general and complete parametric solutions of both finite closed-loop eigenvector matrices and feedback gain matrices are derived. The parametric approach utilizes directly original system data, involves manipulations only on n-dimensional matrices, and reveals all the design degrees of freedom which can be further utilized to achieve certain additional system specifications. A numerical example shows the effect of the proposed approach.

Eigenstructure assignment of lower-order dynamical compensatorsfor linear systems with unknown inputs

Presents a systematic design method of reduced order dynamical compensator via the parametric representations of eigenstructure assignment for linear system, which provides maximum degree of freedom, and can be easily used for the design of a linear system with unknown inputs under some conditions. Even when these conditions are not satisfied, the lower order dynamical compensator can also be designed under some relaxed conditions. Some examples illustrate that the method is neat, simple and effective.

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 related results of continuous and discrete time systems into the delta framework. The efficiency of the design method is illustrated by a numerical example.

Unified parametric approaches for high-order integral observer design for matrix second-order linear systems

A type of high-order integral observers for matrix second-order linear systems is proposed on the basis of generalized eigenstructure assignment via unified parametric approaches. Through establishing two general parametric solutions to this type of generalized matrix second-order Sylvester matrix equations, two unified complete parametric methods for the proposed observer design problem are presented. Both methods give simple complete parametric expressions for the observer gain matrices. The first one mainly depends on a series of singular value decompositions, and is thus numerically simple and reliable; the second one utilizes the fight factorization of the system, and allows eigenvalues of the error system to be set undetermined and sought via certain optimization procedures. A spring-mass-dashpot system is utilized to illustrate the design procedure and show the effect of the proposed approach.

Global stabilizing controller design for linear time-varying systems and its application on BTT missiles

A parametric method for the gain-scheduled controller design of a linear time-varying system is given. According to the proposed scheduling method, the performance between adjacent characteristic points is preserved by the invariant eigenvalues and the gradually varying eigenvectors. A sufficient stability criterion is given by constructing a series of Lyapunov functions based on the selected discrete characteristic points. An important contribution is that it provides a simple and feasible approach for the design of gain-scheduled controllers for linear time-varying systems, which can guarantee both the global stability and the desired closed-loop performance of the resulted system. The method is applied to the design of a BTT missile autopilot and the simulation results show that the method is superior to the traditional one in sense of either global stability or system performance.

Design of Luenberger function observer with disturbance decoupling for matrix second-order linear systems-a parametric approach

A simple method for disturbance decoupling for matrix second-order linear systems is proposed directly in matrix second-order framework via Luenberger function observers based on complete parametric eigenstructure assignment. By introducing the H2 norm of the transfer function from disturbance to estimation error, sufficient and necessary conditions for disturbance decoupling in matrix second-order linear systems are established and are arranged into constraints on the design parameters via Luenberger function observers in terms of the closed-loop eigenvalues and the group of design parameters provided by the eigenstructure assignment approach. Therefore, the disturbance decoupling problem is converted into an eigenstructure assignment problem with extra parameter constraints. A simple example is investigated to show the effect and simplicity of the approach.

Observer-based H_∞ Filtering of 2-D Singular System Described by Roesser Models

This paper discusses the problem of the H∞ filtering for discrete time 2-D singular Roesser models (2-D SRM). The purpose is to design an observer-based 2-D singular filter such that the error system is acceptable, jump modes free and stable, and satisfies a pre-specified H∞ performance level. By general Riccati inequality and bilinear matrix inequalities (BMI), a sufficient condition for the solvability of the observer-based H∞ filtering problem for 2-D SRM is given. A numerical example is provided to demonstrate the applicability of the proposed approach.

Delta算子系统D稳定鲁棒容错控制

研究了Delta算子描述的线性系统基于圆形区域极点配置的鲁棒容错控制(定义作D稳定鲁棒容错控制)问题·利用线性矩阵不等式,给出了Delta算子描述的标称线性系统通过状态反馈实现D稳定容错控制的两个充分条件和D稳定容错控制器的设计方法·利用代数Riccati方程,给出了Delta算子描述的不确定线性系统D稳定鲁棒容错控制的充分条件和D稳定鲁棒容错控制器的设计方法·将连续与离散系统有关该问题的结果统一到了Delta算子框架中·

ON STATE FEEDBACK AND POLE ASSIGNMENT OF THE SECOND ORDER COUPLED SINGULAR DISTRIBUTED PARAMETER SYSTEMS IN HILBERT SPACE

联合单个分布式的参数系统在 Hilbert 空格经由功能的分析和操作符理论被讨论的第二份订单的州的反馈和杆赋值，在哪个无限许多杆被改变。这个问题和答案的建设性的表示的答案被围住的线性操作员的概括的逆给。这研究为学习杆赋值和单个分布式的参数系统的稳定是理论上重要的。

二阶动力学系统的P-D反馈鲁棒极点配置

考虑二阶动力学系统中比例加微分反馈的鲁棒极点配置问题,即求取一比例加微分反馈控制器,在满足闭环系统特性要求的前提下,使得闭环系统特征值关于参数摄动具有最小的灵敏度.基于特征结构配置参数化结果,该问题可转化为含有约束条件的优化问题.给出求解该控制问题的算法,直接基于二阶动力学系统原型,只涉及n-维矩阵计算,便于工程应用.三级质量弹簧系统的仿真表明所提方法的有效性.

基于观测器的不确定广义系统D稳定极点配置

研究了具有D稳定约束的不确定广义系统鲁棒状态观测器问题 .基于参数矩阵不等式和广义逆理论 ,提出了一种广义鲁棒状态观测器的设计方法 ,目的是对于所有容许的参数不确定性 ,相应的广义状态估计系统是正则、无脉冲 ,且其有限极点配置在预先给定的圆盘中 ,从而使整个观测过程具有所希望的鲁棒性和暂态性能 ;

2-D正线性系统的实现问题

讨论广义 2 D系统的正实现问题 .首先引进了 2 D主项系统的定义 ,给出了广义 2 D主项系统传递函数阵分解为正则部分和广义部分的方法 .然后分别讨论了各部分存在正实现的条件和实现的方法 .

不确定奇异分布参数系统的鲁棒D稳定

研究奇异分布参数系统的鲁棒D稳定和D稳定化问题。通过采用配置点谱方法和差分方法,把奇异分布参数系统转换成离散奇异系统。当所有系统矩阵都存在范数有界的不确定性包括差分矩阵E。假设E对于所有允许的不确定性都是秩不变的。这样把该系统的鲁棒分析问题分为两种情况：右奇异和左奇异。基于上面两种情况提出2个充要D稳定条件。这样基于这些条件,采用增广方法,提出充分的D稳定化条件。所有得到的条件都是基于线性矩阵不等式。最后,使用非稳态1维方腔流的数学模型来证明基于两种情况提出的方法的有效性。

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 .