一类离散时间线性切换系统的二次鲁棒镇定

针对一类具有范数有界时变不确定性的离散时间线性切换系统,研究了其二次稳定化状态反馈控制律的设计问题.利用多李亚普诺夫函数法推导了在任意切换下二次稳定化控制律存在的充分条件,该条件被进一步等价地表示成线性矩阵不等式的可解性问题.同时它的解提供了二次稳定化控制律的一个参数化表示.仿真结果验证了所提方法的有效性.     

对称循环组合系统的几个控制问题

研究了对称循环组合系统的输出调节问题和不确定对称循环组合的二次稳定性和二次稳定化问题。结果表明,由于对称循环组合系统结构的特殊性,这的输出调节问题可以转化为一些低价系数的输出调节问题。而不确定对称循环组合系统的二次稳定性可以通过考察若干个低价系数的二次稳定性来判断,且其稳定比化控制律也可以通过低价系数的稳定化控制律来构造。     

离散时滞系统的无记忆稳定化控制器设计

对离散时滞系统,研究无记忆状反馈稳定化控制律的设计问题,导出了控制律存在的条件,并证明了该条件等价于一个线性矩阵不等式系统的可解性问题。通过这个线性矩阵不等式系统的可行解,给出了稳定化控制律的构造方法,进而,通过建立和求解一个凸优化问题,提出了具有较小反馈增益参数的无记忆状态反馈控制律的设计方法。     

关于不确定对称组合系统的稳定化

研究不确定对称组合系统的二次稳定化问题,给出这类系统可二次稳定的一些充分条件及计算反馈控制律的方法.这些条件的检验和反馈控制律的计算都由两个低阶系统关于相应问题的求解来完成.     

线性不确定系统的最优保性能控制--线性矩阵不等式处理方法

针对一类具有范数有界时变参数不确定性的线性系统的和一个给定的二次型性能指标,研究了其最优保性能控制问题,用一个线性矩阵不等式系统的可解性给出了存在保性能状态反馈控制律的条件,并且这个线性矩阵不等式系统的可行解提供了一组保性能控制律的一个参数化表示,进而保性能控制律的这一刻划被用来求解最优保成本控制问题。     

不确定离散时滞系统的保性能控制

针对一类具有范数有界不确定性和状态滞后的离散时间线性系统,结合一个二次型性能指标,采用线性矩阵不等式方法,提出了无记忆状态反馈保性能控制律的存在条件,并利用一个线性矩阵不等式的解给出了保性能控制律的一个参数化表示.     

考虑执行机构故障的离散系统可靠保性能控制设计

对一类离散时间线性时不变系统,研究当执行机构发生连续增益故障情况下的可靠保性能状态反馈控制律的设计问题.应用线性矩阵不等式处理方法,导出系统存在可靠保性能控制律的一个充分条件,进而用一个线性矩阵不等式的可行解给出所有可靠保性能控制律的一个参数化表示.在此基础上,通过建立和求解由一组线性矩阵不等式所表示的凸优化问题,得到最优可靠保性能控制律的设计方法.     

LQ终端控制的生成函数法与Riccati变换法的等价性

通过定义线性哈密顿系统新形式的第3类生成函数, 建立了求解线性二次终端控制问题的生成函数方法与Riccati变换方法的直接联系, 并证明两种方法导出的最优控制律是等价的. 生成函数方法的优势在于可以灵活地处理边界约束条件. 本文根据Riccati变换方法沿时间逆向求解问题的特点, 定义了适于逆向正则变换的第3类生成函数, 用于求解哈密顿两点边值问题, 可得到用生成函数表示的最优控制律. 并通过验证生成函数方法所得最优控制律的各部分与Riccati变换法所得的结果相对应, 证明了两种方法所得控制律的等价性.     

线性时滞系统前馈-反馈次优控制: Taylor 级数法

研究线性时滞系统最优控制的前馈反馈近似设计问题.基于Taylor级数法,将系统的二次型最优控制问题转化为线性代数方程组的求解问题,给出了系统前馈反馈次优控制律的存在唯一性条件和Taylor级数表示形式.仿真算例验证了方法的有效性.     

一类切换组合系统的分散反馈镇定

首次提出切换组合系统的概念,给出了使此系统渐近稳定的分散切换控制律的设计,研究了带有连续控制量的组合大系统采用分散混杂状态反馈稳定化问题.     

不确定广义系统的保性能控制

针对一类具有范数有界不确定性的连续广义系统和一种具有时间乘积形式的二次性能指标,研究其状态反馈保性能控制器的设计问题.这种性能指标能够使系统状态响应随着时间的增加更快地趋于零,从而缩短系统达到稳定所需要的时间.文中给出了最优保性能控制器存在的充分必要条件并基于双线性矩阵不等式(BMI)、二次矩阵不等式(QMI)和LMI给出其设计方法,最后利用SDP软件和BMI软件举例说明所得结论的可行性.     

A stabilizing output-feedback linear quadratic control for pure input-delayed systems

This paper proposes the design of a stabilizing output-feedback linear quadratic controller for a pure input-delayed system. By reducing a pure input-delayed system into a non-delayed system and modifying the linear quadratic cost, a simple, stabilizing output-feedback linear quadratic controller is formulated in terms of linear matrix inequalities. The worst-case output-feedback LQ controller is also presented with respect to the unknown initial states. A numerical example is given to illustrate the performance of the proposed controllers.     

Suboptimal Control of Rigid Body Motion with a Quadratic Cost

In this paper we consider the problem of controlling the rotational motion of a rigid body using three independent control torques. Given a quadratic cost we seek stabilizing state feedback controllers which guarantee that all motions starting within a specified bounded set have cost less than a given number; i.e., we seek suboptimal stabilizing controllers. For a special class of cost functions, we present explicit expressions for suboptimal stabilizing controllers yielding a cost arbitrarily close to the infimal cost. For the general case, we present sufficient conditions which guarantee the existence of linear, suboptimal, stabilizing controllers.     

A new LMI-based approach to relaxed quadratic stabilization of T-S fuzzy control systems

This paper proposes a new quadratic stabilization condition for Takagi-Sugeno (T-S) fuzzy control systems. The condition is represented in the form of linear matrix inequalities (LMIs) and is shown to be less conservative than some relaxed quadratic stabilization conditions published recently in the literature. A rigorous theoretic proof is given to show that the proposed condition can include previous results as special cases. In comparison with conventional conditions, the proposed condition is not only suitable for designing fuzzy state feedback controllers but also convenient for fuzzy static output feedback controller design. The latter design work is quite hard for T-S fuzzy control systems. Based on the LMI-based conditions derived, one can easily synthesize controllers for stabilizing T-S fuzzy control systems. Since only a set of LMIs is involved, the controller design is quite simple and numerically tractable. Finally, the validity and applicability of the proposed approach are successfully demonstrated in the control of a continuous-time nonlinear system.     

Stabilizing fuzzy system models using linear controllers

A Lyapunov-based approach is used to derive a sufficiency condition for stabilizing a class of fuzzy system models using linear controllers. A design algorithm for constructing stabilizing linear controllers is given. The results obtained are illustrated with a design of a linear stabilizing controller for a system consisting of an inverted pendulum mounted on a cart. The controller is designed using a fuzzy model of the system and tested on the original system model     

Trajectory-based design of robust non-fragile controllers for a class of uncertain linear continuous-time systems

This paper deals with a design problem of robust non-fragile stabilizing controllers for a class of uncertain linear continuous-time systems. The proposed design approach of robust non-fragile controllers is based on computation of the trajectory for the uncertain linear system and differs from the existing methods based on quadratic stabilization via Lyapunov criterion. In this paper, we show that sufficient conditions for asymptotical stability of the linear system with uncertainties and controller gain variations, and a LMI-based design algorithm of a robust non-fragile controller. Furthermore, we extend the result to the design problem of decentralized robust non-fragile controllers for a class of uncertain large-scale interconnected systems. Finally, the effectiveness of the proposed design scheme of robust non-fragile controllers is shown through illustrative examples.     

Petersen’s lemma on matrix uncertainty and its generalizations

Various generalizations and refinements are proposed for a well-known result on robust matrix sign-definiteness, which is extensively exploited in quadratic stability, design of robustly quadratically stabilizing controllers, robust LQR-problem, etc. The main emphasis is put on formulating the results in terms of linear matrix inequalities.     

基于强传递性的线性时不变系统同时稳定化的充分条件

本文考虑了离散线性时不变系统的同时稳定化问题.基于强传递性的方法,本文利用互素因子分解法建立了同时存在多个稳定控制器的充分条件.此外,在这个条件下,本文提出了同时稳定3个系统的控制器的设计方法.最后,给出了一个例子验证结果的有效性.     

Remarks on strong stabilization and stable H/sup /spl infin// controller design

A state space based design method is given to find strongly stabilizing controllers for multiple-input-multiple-output plants (MIMO). A sufficient condition is derived for the existence of suboptimal stable H/sup /spl infin// controller in terms of linear matrix inequalities (LMIs) and the controller order is twice that of the plant. A new parameterization of strongly stabilizing controllers is determined using linear fractional transformations (LFTs).