不确定离散线性系统的鲁棒镇定

针对一类具有范数有界时变不确定性的离散性线系统,研究其二次稳定化状态反馈控制律的设计问题。推导出二次稳定化控制律存在一个充分必要条件,该条件被塌一步等价地表示成一个线性矩阵不等式的可解性问题。后者可用现有方法方便地求解,且它的解提供了所有二次稳定定化控制律的一个参数化表示。     

凸锥型不确定线性切换系统的二次镇定

研究具有凸锥型不确定性的线性切换系统的二次鲁棒稳定化问题.这种不确定性是由若干已知常数矩阵所张成的凸锥构成的.利用凸组合技术,分别给出了连续和离散线性切换系统的鲁棒二次可稳定条件及切换律的设计方法.按照这些条件,只要判断张成凸锥的顶点矩阵的某个凸组合是否可稳即可.最后给出仿真例子.     

非线性切换系统的二次镇定

研究多输入多输出非线性切换系统在任意切换律下的二次镇定问题.当非线性切换系统有一致规范型,且一致规范型的零动态在任意切换律是渐近稳定时,设计出状态反馈控制律,并构造出所有闭环子系统的共同二次Lyapunov函数,实现了这类多输入多输出非线性切换系统在任意切换策略下的二次可镇定性,所得结果也适用于线性切换系统。     

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.     

一类线性切换系统具有H∞性能指标的二次稳定

研究了一类线性切换系统具有H_∞扰动衰减度二次稳定问题.这类线性切换系统由两个子系统组成,并且每个子系统都不是具有H_∞扰动衰减度二次稳定的.利用单Lyapunov函数方法,得到了线性切换系统具有H_∞扰动衰减度二次稳定的充分条件,同时由凸组合系统设计出确保线性切换系统二次稳定且具有H_∞扰动衰减度的切换律.进一步,还给出了线性切换系统具有H_∞扰动衰减度二次稳定的必要条件.最后的仿真实例表明了结论的有效性.     

三阶切换系统的镇定

研究了三阶切换系统的镇定问题. 给出三阶线性控制系统，以给定的正定矩阵[WTHX]M[WTBZ]作为二次李亚普诺夫函数的新的充分条件. 然后, 证明了在适当条件下三阶切换系统是二次可镇定的. 文中设计出镇定三阶切换系统的反馈控制律, 并提出了解决二次镇定问题的直接算法.     

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。     

参数不确定马尔可夫跳变系统的鲁棒适应控制

针对具有参数不确定的线性马尔可夫跳变系统的鲁棒适应控制问题进行了研究.分析了切换系统切换律的可观测和不可观测情形.对于可观测的切换律,利用线性矩阵不等式和共同二次Lyapunov函数方法,得出的具有参数不确定的切换系统是鲁棒可镇定的;对于切换律符合不可观测的马尔可夫随机过程的情况,通过设计恰当的采样适应控制器得到系统随机可镇定的充分条件.并通过例子给出适应镇定控制器的算法.     

一类多输入级联非线性切换系统的全局镇定

研究一类带有部分线性系统的多输入级联非线性切换系统的全局镇定问题. 首先, 给出保证线性部分有一致规范型的充分条件. 其次, 利用一致规范型及其零动态的共同二次Lyapunov函数设计状态反馈使得线性部分在任意切换律下镇定. 最后, 通过构造共同Lyapunov函数能实现闭环系统在任意切换律下的全局渐近稳定性.     

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。     

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。     

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.     

一类时滞系统的绝对稳定性问题研究

基于线性矩阵不等式处理方法,研究了一类具有扇形非线性关联的时滞系统绝对稳 定性问题.导出了用一个线性矩阵不等式系统的可行性表示的绝对稳定性滞后依赖型条件,进 而,通过求解一组线性矩阵不等式,给出使得闭环系统绝对稳定的无记忆状态反馈控制律设计 方法,最后用例子验证了文中提出的结果.     

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).     

一类不确定模糊动态时滞系统保成本控制

针对一类不确定非线性动态时滞系统，利用模相T—S模型，通过状态反馈对保成本控制问题进行研究。应用线性矩阵不等式给出模糊闭环系统渐近稳定的充分条件，保证了所有允许的不确定闭环系统是稳定的，而且对于一个给定的二次型成本函数，舱保证闭环成本不超过某个界。仿真结果表明所提出的控制方法是有效的。     

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。     

Stable and Quadratic Optimal Control for TS Fuzzy-Model-Based Time-Delay Control Systems

For the finite-horizon optimal control problem of the Takagi-Sugeno (TS) fuzzy-model-based time-delay control systems, by integrating the delay-dependent stabilizability condition, the shifted-Chebyshev-series approach (SCSA), and the hybrid Taguchi-genetic algorithm (HTGA), an integrative method is presented to design the stable and quadratic optimal parallel distributed compensation (PDC) controllers. In this paper, the delay-dependent stabilizability condition is proposed in terms of linear matrix inequalities (LMIs). Based on the SCSA, an algebraic algorithm only involving the algebraic computation is derived in this paper for solving the TS fuzzy-model-based time-delay feedback dynamic equations. In addition, by using the SCSA, the stable and quadratic optimal PDC control problem for the TS fuzzy-model-based time-delay control systems is replaced by a static parameter optimization problem represented by the algebraic equations with constraint of the LMI-based stabilizability condition, thus greatly simplifying the stable and optimal PDC control design problem. The computational complexity for both differential and integral in the stable and optimal PDC control design of the original dynamic systems may therefore be reduced considerably. Then, for the static constrained optimization problem, the HTGA is employed to find the stable and quadratic optimal PDC controllers of the TS fuzzy-model-based time-delay control systems. A design example of the stable and quadratic optimal PDC controllers for the continuous-stirred-tank-reactor system is given to demonstrate the applicability of the proposed integrative approach.     

Linear quadratic suboptimal control with static output feedback

This paper considers the design of a stabilizing static output feedback gain which keeps linear quadratic (LQ) performance index less than a specified number (we call this an ‘LQ suboptimal controller’). Existence of such a controller is shown to be equivalent to the existence of a positive-definite matrix P such that P satisfies two linear matrix inequalities (LMIs) while P⁻¹ satisfies another LMI. All LQ suboptimal controllers are explicitly parametrized by the freedom in the choice of the positive-definite matrix P satisfying the LMIs, and an arbitrary positive scalar and an arbitrary matrix of fixed dimension with a norm bound. A modified version of the min/max algorithm is given to find a positive-definite solution P to the LMIs.     

不确定多时滞离散切换系统的输出反馈镇定

针对一类具有多重状态时滞和凸多面体不确定性的离散切换系统,研究该系统在任意切换信号下基于状态观测器的输出反馈鲁棒镇定问题.首先通过状态变量的替换将多时滞项转变成不含时滞项,再利用分段Lyapunov函数和线性矩阵不等式方法,导出凸多面体不确定多时滞离散切换系统基于观测器的输出反馈鲁棒镇定的充分条件,并将此条件转化成为一组线性矩阵不等式的可行性问题,同时给出基于状态观测器的输出反馈控制器.仿真结果表明设计方法是可行有效的.