线性系统静态输出反馈镇定的LMI方法

利用无约束条件的线性矩阵不等式（LMI）研究了W－问题和P－问题,而后者的解可用来设计静态输出反馈（SOF）镇定控制,作为一个应用考虑了不确定系统的静态输出反馈问题,给出了依赖于LMI条件的SOF设计方法。     

模糊不确定时滞系统的静态输出的反馈镇定:迭代线性矩阵不等式方法

对一类不确定非线性时滞系统利用模糊T＿S模型进行建模,研究了静态输出反馈镇定问题.用矩阵不等式的形式给出了模糊T＿S不确定时滞系统可通过静态输出反馈镇定的充分条件.并将矩阵不等式的条件转化为迭代线性矩阵不等式(ILMI),并给出相应的算法.     

基于LMI的分布时滞系统输出动态反馈镇定

研究分布时滞系统的输出动态反馈镇定问题. 基于闭环系统的中立型变换及相应Lyapunov-Krasovskii泛函的构造与解析技巧, 建立了与时滞相关的控制器存在性判据. 在此基础上通过控制器参数化设计方法, 将控制器参数的求解归结为线性矩阵不等式解的形式. 仿真算例验证了方法的有效性     

静态输出反馈控制的一种数值解法

在基于目标函数线性化的序列线性规划矩阵方法（SLPMM）的框架下,研究了线性时不变系统静态 输出反馈（SOF）H￥ 控制问题的数值解法,提出了一种改进的SLPMM 算法：通过求解一个LMI 特征值问题得到 SLPMM 算法的初始解,减少了运算的迭代次数,并同时给出了对H￥ 范数的一个初始估计．文中给出了基于该算法 的静态输出反馈H￥ 控制问题的详细求解步骤,最后用一个飞机纵向控制器的设计实例说明算法的有效性．     

不确定系统静态输出反馈可靠控制

针对含有状态不确定项的线性系统,提出具有执行器故障的静态输出反馈控制问题。首先给出在不考虑故障时设计控制器使系统保持渐近稳定的充分条件;然后讨论对于同一系统同一控制器在考虑执行器故障时系统出现不稳定;接下来,针对同一故障模型重新设计静态输出反馈控制器使系统在发生故障后仍保持渐近稳定。最后,数值仿真验证了本文结果的有效性。     

基于比较原理的非线性组合系统的输出反馈镇定

综合运用比较原理和LMI方法,通过构造一比较系统,将原组合系统的稳定性问题转化为维数较低的比较系统的稳定性问题,并利用M矩阵特性导出了比较系统稳定的一个充分条件．为了求取输出反馈增益,建立了等价稳定条件的QLMI表示形式．这一方法的特点是使大系统的稳定控制器设计的复杂度保持在子系统一级的水平上．数值实例说明了所提出算法在实际工程应用中的可行性和有效性．     

一类线性系统区域极点配置静态输出反馈可靠控制

考虑连续线性系统,在连续增益故障模型的前提下,提出带有执行器故障的圆形区域极点配置的静态输出反馈的可靠控制问题。本文利用线性矩阵不等式(LMI) 在考虑执行器故障模型的基础上,给出圆形区域极点配置的静态输出反馈的可靠控制器存在的充分条件。通过成果的仿真,并进一步说明当系统发生故障时,正常控制的闭环系极点可能离开所给定的圆形区域,而可靠控制的闭环系统仍然会保持极点在给定的圆形区域内。从而看出对系统进行极点配置的静态输出反馈的可靠控制的必要性。     

基于输出反馈的直升机变结构控制律设计

针对直升机的小扰动模型,设计了静态输出反馈滑模控制器（SOFSMC）。利用参考模型,实现了直升机的相关动态指标。针对滑模面的设计问题,将其等价地转化为一组双线性矩阵不等式（BLMI）,并采用迭代线性矩阵不等式（ILMI）技术来求解。针对控制律的综合问题,给出了一种基于单位向量法的控制律,并通过引入线性反馈来保证系统进入滑动模态后线性控制部分与标称系统的线性控制部分的一致性。仿真结果验证了该方法的有效性。     

一类不确定线性时滞系统的输出反馈鲁棒镇定

研究一类不确定线性时滞系统的输出反馈鲁棒镇定问题,其中不确定性不必满足匹配条件。以二次Lyapunov泛函保证系统的渐近稳定性,利用线性矩阵不等式给出了系统可以利用动态输出反馈鲁棒镇定的充分条件。当此条件成立时,基于线性矩阵不等式的解构造了全阶动态输出反馈镇定控制器。     

Static output feedback control of positive linear systems with output time delays

ABSTRACT

In this paper, we discuss a new problem of static output feedback controllers design for positive systems with delayed output measurements. When delayed output measurements are exclusively used as feedback control signals, previous control design methods for positive systems relying on the so-called delay-independent positivity and stability conditions are unable to synthesise a stable static output feedback controller for positive systems. A new method based on delay-dependent positivity and stability conditions is proposed in this paper to tackle this issue. We show that the synthesis of static output feedback controllers for positive systems under the effect of delayed output measurements is feasible under the newly proposed design method. Numerical examples are given to demonstrate the effectiveness of the new result.     

基于谱技术的随机系统的区间输出反馈镇定控制

基于谱技术研究了线性随机系统的区间稳定性与镇定控制问题.首先给出了保证随机系统区间稳定的充分性判据,该判据可确保随机系统的谱全部位于左半复平面的某一带状区域内;然后,利用矩阵的奇异值分解给出了静态输出反馈镇定控制器的设计方法,并将其归结为一组线性矩阵不等式（LMIs）的求解问题;最后,数值仿真验证了所得结论的正确性.     

Static output feedback control for positive linear continuous‐time systems

This paper studies the problem of designing the static output feedback controller for the positive linear continuous‐time systems. On the basis of a system augmentation approach, a novel characterization on the stable condition of the closed‐loop system is firstly established. Then, a necessary and sufficient condition is given to ensure the existence of the desired static output feedback controller, and an iterative linear matrix inequality algorithm is presented to compute the feedback gain matrix. Finally, a numerical example is provided to illustrate the effectiveness of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.     

New characterisations of positive realness and static output feedback control of discrete-time systems

This article is concerned with the problems of positive real analysis and control synthesis for discrete-time systems. New linear matrix inequality (LMI) characterisations of positive realness are derived, which enable one to check the positive realness by using parameter-dependent Lyapunov function. The relationship between the proposed characterisations and the existing ones are clarified, which shows that our new results are of less conservatism for characterising the positive realness of discrete-time systems with polytopic uncertainty. In addition, sufficient conditions for static output feedback positive real controller design are given in terms of solutions to a set of linear matrix inequalities. Numerical examples are included for illustration.     

连续不确定模糊系统的静态输出反馈控制

对于一类状态矩阵、输入矩阵和扰动输入矩阵中均含有不确定项的连续T-S模糊系统,研究其静态输出反馈控制问题.用矩阵不等式的形式给出了该模糊系统可通过静态输出反馈控制稳定的充分条件,并将矩阵不等式的条件转化为迭代线性矩阵不等式,同时给出了相应的迭代算法.最后用数值仿真例子说明了该算法的有效性和收敛性.     

Simultaneous linear-quadratic optimal control design via static output feedback

In this paper, the problem of designing a fixed static output feedback control law which minimizes an upper bound on linear quadratic (LQ) performance measures for r distinct MIMO plants is addressed using linear matrix inequality (LMI) technique. An iterative LMI algorithm is proposed to obtain the solution. Examples are used to demonstrate its effectiveness. Copyright ©1999 John Wiley & Sons, Ltd.     

Hermite matrix in Lagrange basis for scaling static output feedback polynomial matrix inequalities

Using Hermite's formulation of polynomial stability conditions, static output feedback (SOF) controller design can be formulated as a polynomial matrix inequality (PMI), a (generally nonconvex) nonlinear semidefinite programming problem that can be solved (locally) with PENNON, an implementation of a penalty and augmented Lagrangian method. Typically, Hermite SOF PMI problems are badly scaled and experiments reveal that this has a negative impact on the overall performance of the solver. In this note we recall the algebraic interpretation of Hermite's quadratic form as a particular Bézoutian and we use results on polynomial interpolation to express the Hermite PMI in a Lagrange polynomial basis, as an alternative to the conventional power basis. Numerical experiments on benchmark problem instances show the improvement brought by the approach, in terms of problem scaling, number of iterations and convergence behaviour of PENNON.     

含未知输入的时滞系统的函数观测器及输出反馈镇定

考虑了含未知输入的时滞系统的线性函数观测器设计.在一个不失一般性的秩条件假定下,以线性矩阵不等式(LMI)的形式给出了观测器存在的时滞无关型及时滞相关型判据,进而得到函数观测器改进的设计方法.此外,还讨论了降维状态观测器的设计,给出了基于观测器的反馈镇定控制器,实现了闭环的特征根分离及内稳定.具体算例说明了本文方法的有效性.     

Decay rate constrained stabilization of positive systems using static output feedback

This paper investigates the stabilization problem by means of a static output feedback control for positive systems with/without interval uncertainties. The designed closed‐loop system is ensured to be positive and stable with a prescribed decay rate. Necessary and sufficient conditions for the existence of such controllers are established in terms of linear matrix inequalities together with a matrix equality constraint. Furthermore, the desired static output feedback controllers can be derived directly via the cone complementarity linearization techniques. Finally, an illustrative example is presented to show the validity of results obtained in this paper. Copyright © 2010 John Wiley & Sons, Ltd.