仿射非线性奇异系统的分析

从机器人控制中抽象出一类仿射非线性广义系统,给出此类系统的简化条件及方法,讨 论了它的输出跟踪问题,并推出了可稳的充分条件.     

基于结构L yapunov 矩阵的静态输出反馈镇定

线性时不变系统的静态输出反馈控制可行性等价于两个耦合的线性矩阵不等式解的存在性问题，这导致了一个非线性最优化问题，是无法直接求解的．针对线性时不变系统(LTI)，深入研究这两个矩阵不等式的关系，通过构造一个结构Lyapunov矩阵，给出了一个问题有解的充分条件，并在此基础上提出一个静态输出反馈镇定算法．利用线性矩阵不等式(LMI)方法，可直接求解出相应的输出反馈增益．数值实例证明了该方法的有效性．     

线性离散周期奇异系统的可解性与渐近稳定性

讨论了线性离散周期奇异系统初值问题的可解性和渐近稳定性问题.首先分析总结了线性离散变系数奇异系统可解性及其广义状态解的一般概念.在此基础上,定义了线性离散变系数奇异系统的一致渐近稳定性,并通过增加系统维数把线性离散周期奇异系统转化为线性定常奇异系统,从而得到了线性离散周期奇异系统可解和一致渐近稳定的充要条件.     

五对角矩阵的特征值反问题

本文讨论了一类由五个特征值和相应特征向量构造实对称五对角矩阵的特征值反问题.研究了解的存在性以及存在解的充分必要条件,而且给出了算法和数值例子.     

New criterion for generalized diagonally dominant matrices and M-matrices

We provide some new sufficient and necessary conditions for identifying generalized (strictly) diagonally dominant matrices and obtain some criteria for judging (nonsingular) M-matrices.     

实际意义下n-D单边矩阵方程有解的充要条件

本文在讨论n-D矩阵方程求解条件的基础上, 针对由Agathoklis等人提出的具有实际意义的n维（n-D）离散系统,给出了判定n-D矩阵 方程是否有解的充要条件,并给出了判定系统是否具有实际意义稳定性的方法,以算例加以 说明．     

Variable structure output feedback control design for a class of uncertain dynamic systems

In this paper, we consider the problem of designing a variable structure output feedback control (VSOFC) law for a class of uncertain systems with mismatched uncertainty in the state matrix. We derive existence conditions of linear sliding surfaces in terms of constrained linear matrix inequalities (LMIs), and we give VSOFC strategies. We also give a simple design procedure and parameterizations of the linear switching surfaces, together with solvability conditions for the given constrained LMIs. Finally, we give a design example in order to show the effectiveness of our method.     

线性时滞系统的耗散控制

研究了一类线性时滞系统的二次耗散控制问题,基于线性矩阵不等式（LMI）方法导出了耗散控制器存在的充分条件,通过线性矩阵不等式的可行解构造出耗散态状态反馈和动态输出反馈控制律,相应的闭环系统是二次稳定和严格（Q,S,R）耗散的,本文的主要贡献是统一了线性时滞系统现有的H∞控制和无源控制结果。     

Structured time-delay systems: A graph approach

In this paper, linear structured systems with delays are defined and a simple graph representation for these systems is given. Then, the generic controllability of time-delay systems is introduced and a graph criterion for controllability is provided. The generic row-by-row decoupling problem without prediction of such systems is then studied and graphical necessary and sufficient solvability conditions for this problem is derived.     

一类不确定系统的鲁棒稳定性分析

研究了一类不确定系统的稳定性问题, 以线性矩阵不等式(LMI)的形式给出了该类系统的鲁棒稳定条件, 并将该结果推广到区间系统的稳定性分析, 提出了研究区间系统稳定性问题的新方法, 给出了线性矩阵不等式形式的稳定判据, 该判据将区间系统的稳定性问题转化为一类线性矩阵不等式的可解问题. 最后通过仿真算例验证了本文结果具有更小的保守性.     

Output regulation of linear plants subject to constraints

Output regulation problems for continuous-time linear systems with state and/or input constraints are studied. The problems are formulated in global and semi-global setting by using state or full information feedback. The goal of this paper is to develop solvability conditions for the posed problems. Moreover, appropriate regulators are constructed under the solvability conditions. To state the solvability conditions clearly, a taxonomy of constraints is introduced which delineates the constraints into several categories. Such a taxonomy of constraints provides a classification of linear plants with constraints and identifies what types of output regulation problems are solvable. Results developed here include as a special case the results obtained in the literature for systems with only input constraints. The constraint taxonomy also identifies some intrinsically hard constraints (non-right invertible constraints) for which the solvability conditions of global/semi-global output regulation problems are not clear yet. As a special case of output regulation, we also consider tracking problems with constraints. It is shown that if there exists a state feedback controller with a stabilizing domain of attraction, then one can find a regulator with a tracking domain of attraction arbitrarily close to the stabilizing domain.     

Generalized invariant subspaces and parameter insensitivedisturbance-rejection problems with static output feedback

In the geometric approach some generalized invariant subspaces for uncertain linear systems are investigated, and then various parameter insensitive disturbance-rejection problems with static output feedback are formulated and necessary and sufficient conditions for the problems to be solvable are presented. Further, some sufficient conditions which are useful to check the solvability conditions are presented using the notions of generalized invariant subspaces     

A graph-theoretic approach to fault detection and isolation for structured bilinear systems

In this paper, using a graph-theoretic approach, we address some issues related to the fault detection and isolation for structured bilinear systems. Considering a structured bilinear system submitted to faults and disturbances, we give necessary and sufficient conditions to the solvability of the so-called bilinear fundamental problem of residual generation. We also treat the cases where the system is submitted to multiple failures occurring simultaneously or only one at a time. One of the main advantages of the proposed analysis tool is that all the given conditions are easy to check because they deal with finding paths in a digraph. This makes our approach well suited to studying large scale systems.     

周期时变线性系统的一般线性二次型最优控制

讨论周期时变线性系统的一般线性二次型最优控制问题, 即状态方程为非齐次方程且二次型性能指标包含线性项的一般情况. 给出了该问题可解的一系列充分必要条件, 同时给出了最优控制的解析构造以及最优性能指标值.     

Solvability conditions and general solution for mixed Sylvester equations

In this paper, we give some necessary and sufficient solvability conditions for the mixed Sylvester matrix equations, and parameterize general solution when it is solvable. Moreover, we investigate the maximal and minimal ranks of the general solution, and maximal and minimal ranks and inertias of Hermitian part of solution, respectively.     

Solving EP singular linear systems

In this article, we deal with EP matrix and EP singular linear systems. We give some properties of EP matrix and its generalized inverse, analyze the solutions of EP systems and make some applications in Navier-Stokes equations.     

New approaches to relaxed stabilization conditions and H-infinity control designs for T-S fuzzy systems

This paper focuses on the problem of fuzzy control for a class of continuous-time T-S fuzzy systems.New methods of stabilization design and H infinity control are derived based on a relaxed approach in...     

Guaranteed roll-off in a class of high-gain feedback design problems

A number of synthesis problems associated with (almost) disturbance decoupling by state or measurement feedback is considered. Starting from a mathematical definition of the notion of high-frequency roll-off, known results on the solvability of these problems are generalized to the situation in which we require their solvability together with a certain guaranteed roll-off between disturbance and control. The conditions are formulated in terms of the solvability and approximate solvability of certain matrix equations in rational functions.     

Sensor Location for Diagnosis in Linear Systems: A Structural Analysis

We consider here the fault detection and isolation (FDI) problem for linear systems. We are interested in designing a set of observer-based residuals, in such a way that the transfer from the faults to the residuals is diagonal and the transfer from the disturbances to the residuals is zero. We deal with this problem when the system under consideration is structured, that is, the entries of the system matrices are either fixed zeros or free parameters. This problem can be solved in terms of the graph that can be associated in a natural way with a structured system. When the FDI solvability conditions are not satisfied, we assume that internal variables can be measured at a cost and look into the question of wether the problem is solvable with these new measurements. We give solvability conditions for a solution with a minimal number of additional sensors and among such solutions provide a minimal cost solution for the sensor location problem under consideration. We pay particular attention to the internal analysis of the system, and we propose a structural decomposition of the system associated graph based on some particular separators. This analysis leads to the definition of a reduced system. We prove that some potential additional sensors are inefficient for solving our FDI problem and that the FDI problem can be solved using only measurements on the reduced system     

On feedback invariance properties for systems over a principalideal domain

Simple necessary and sufficient conditions for the solvability of many control problems for linear systems over a field are based on the equivalence between the (A, B)-invariance property and the (A+BF)-invariance, or feedback invariance, property. For systems over a ring, this equivalence is no longer true and many results of the geometric control theory cannot be extended. We present new, algorithmically checkable characterizations of the (A+BF)-invariance property for systems defined over a principal ideal domain and a new solvability condition for the disturbance rejection problem