具有时滞互联项的线性不确定系统的分散反馈镇定

文章研究了一类互联项具有时滞的不确定组合大系统,基于系统的状态反馈给出了系统可分散反馈镇定的控制规律。利用线性矩阵不等式给出了系统可分散反馈镇定的充分条件,最后用实例验证了所得结论的正确性。     

基于Riccati-It方程设计线性时滞系统鲁棒控制器的方法

利用Riccati-Ito型矩阵代数方程研究线性时不变系统的状态反馈镇定问题，对时滞系统给出了一种状态反馈镇定方法，这种镇定方法适应于许多时滞系统，其设计方案具有滞后无关性及对于许多系统滞后项系数任意性的完全适应性．本文第二部分研究时不变线性不确定系统的鲁棒镇定，利用Riccati-Ito型矩阵代数方程给出了这类系统鲁棒镇定控制器的设计方法．     

具有时滞的线性奇异系统镇定的Riccati方程方法

本文考虑了具时滞的线性奇异系统的镇定问题，利用Ｒｉｃｃａｔｉ方程方法给出了系统无记忆反馈控制器的设计，并得到了系统可经状态反馈镇定的条件。     

T-S 模糊时滞模型的时滞相关稳定性分析和镇定

研究一类用T—S模糊模型描述的非线性不确定时滞系统的时滞相关鲁棒镇定问题．基于线性矩阵不等式的可行解，首先给出利用T—S模糊模型描述的非线性时滞系统时滞相关稳定性准则；然后给出了经状态反馈鲁棒镇定设计的新方法．所设计的控制器能确保闭环系统渐近稳定．     

基于Riccati-ItXô方程设计线性时滞系统鲁棒控制器的方法*

利用Ｒｉｃｃａｔｉ－Ｉｔｏ型矩阵代数方程研究线性时不变系统的状态反馈镇定问题，对时滞系统给出了一种状态反馈镇定方法，这种镇定方法适应于许多时滞系统，其设计方案具有滞后无关性及对于许多系统滞后项系数任意性的完全适应性，本文第二部分研究对不变线性不确定系统的鲁棒镇定，利用Ｒｉｃｃａｔｉ－Ｉｔｏ型矩阵代数方程给出了这类系统鲁棒镇定控制器的设计方法。     

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.     

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。     

离散时滞切换系统的无记忆状态反馈镇定

针对一类子系统为离散时滞系统的切换系统,研究了稳定性与无记忆状态反馈镇定问题．采用多李雅普诺夫函数法,首先以线性矩阵不等式形式给出了在任意切换信号作用下离散时滞切换系统渐进稳定的一个充分性条件;然后给出了系统无记忆状态反馈镇定的控制器设计方案,并将结果推广到不确定离散时滞切换系统;最后用仿真算例验证了所提出设计方案的可行性。     

时滞线性随机系统的均方稳定性与反馈镇定*

本文研究Ｉｔｏｏ型随机滞后系统的均方稳定性与反馈镇定。文中首先建立了Ｉｔｏ型随机滞后系统的新型稳定性定理，然后采用适当的Ｌｙａｐｕｎｏｖ泛函得到了时滞线性随机系统零解均方渐近稳定的一个充分性判据，该判据适用于完全滞后型的随机系统，据此判据，文中给出了时滞线性随机系统的滞后反馈镇定方法。     

具有状态时滞和控制时滞的不确定性非线性系统的鲁棒控制

对于具有状态时滞和控制时滞的不确定性非线性系统，当其线性部分的不确定性满足范数有界条件而非线性部分的不确定性满足匹配条件时，本文研究其鲁棒镇定问题．在整体指数稳定的意义下，我们得到了上述这类系统可由线性状态反馈和输出反馈镇定的充分条件——某个代数黎卡提不等式有解．并且只要得到了黎卡提不等式的解，就可很方便地设计出对应的控制器．     

分数阶线性定常系统的状态反馈镇定

研究了在分数阶受控系统中稳定性的问题。假定分数阶系统是在线性定常的情况下,利用状态反馈的方法,构造状态反馈矩阵以实现对系统的稳定性控制;给出了分数阶系统由状态反馈镇定的条件及其证明,并给出了状态反馈镇定的综合算法。仿真实例证明了采用状态反馈实现系统镇定的可行性和有效性。     

Complementary results on the stability bounds of singularly perturbed systems

In this note, we will provide a new systematic approach to characterize and compute the stability bound of a singularly perturbed linear system. The approach is based on the feedback system representation of an additional matrix perturbation problem. The idea is to change the stability bound problem to the stability problem of an underlying feedback system. This approach allows multiple choices in formulating the underlying feedback system and thus has the potential of characterizing and computing the stability bound in a number of different ways. By formulating two kinds of different feedback systems, some existing and new results on the stability bounds are derived based on the feedback system approach. The new results complement the existing frequency-domain based stability criteria and make the frequency-domain technique more applicable and useful to the stability bound problem. An example is provided to show the new stability criterion is effective and useful in determining the stability bound.     

Quadratic stabilizability of switched linear systems with polytopic uncertainties

In this paper, we consider quadratic stabilizability via state feedback for both continuous-time and discrete-time switched linear systems that are composed of polytopic uncertain subsystems. By state feedback, we mean that the switchings among subsystems are dependent on system states. For continuous-time switched linear systems, we show that if there exists a common positive definite matrix for stability of all convex combinations of the extreme points which belong to different subsystem matrices, then the switched system is quadratically stabilizable via state feedback. For discrete-time switched linear systems, we derive a quadratic stabilizability condition expressed as matrix inequalities with respect to a family of non-negative scalars and a common positive definite matrix. For both continuous-time and discrete-time switched systems, we propose the switching rules by using the obtained common positive definite matrix.     

On the stability of nonlinear plants that include an observer for their feedback linearization

The states of a plant are required to achieve exact linearization via state feedback and transformation. This calls for an observer when all the plant states are not directly accessible, then the linearizing feedback law can be implemented with the observer estimates. We analyse this situation from a stability point of view, for a class of nonlinear systems and a class of observers. Morever, we set a sufficient condition that makes possible the stabilization of the whole feedback system: the plant, the observer and the (linearizing) feedback law. From this condition, which depends on the observer gains and the linear feedback gains, we find a region for these parameters where the stability of the whole system is guaranteed.     

State and Mode Feedback Control for Discrete-time Markovian Jump Linear Systems With Controllable MTPM

In this note, the state and mode feedback control problems for a class of discrete-time Markovian jump linear systems (MJLSs) with controllable mode transition probability matrix (MTPM) are investigated. In most achievements, controller design of MJLSs pays more attention to state/output feedback control for stability, while the system cost in practice is out of consideration. In this paper, we propose a control mechanism consisting of two parts: finite-path-dependent state feedback controller design with which uniform stability of MJLSs can be ensured, and mode feedback control which aims to decrease system cost. Differing from the traditional state/output feedback controller design, the main novelty is that the proposed control mechanism not only guarantees system stability, but also decreases system cost effectively by adjusting the occurrence probability of system modes. The effectiveness of the proposed mechanism is illustrated via numerical examples.      

一种推广的组合非线性输出反馈控制

针对多变量饱和线性系统的时变参考输入跟踪问题,研究了一种组合非线性输出反馈控制器的设计方法.基于原始的组合非线性反馈理论,构造了全阶和降阶输出反馈控制器.控制器由线性输出反馈项和非线性反馈项组成,使得闭环系统在包含于吸引域的不变集内渐近稳定.除了能够跟踪时变参考输入外,系统还具有良好的动态性能.仿真结果说明了所开发控制器的有效性.     

Global quadratic stabilization of a class of nonlinear systems

The problem of quadratic stabilization for a class of nonlinear systems is examined in this paper. By employing a well-known Riccati approach, we develop a technique for designing a state feedback control law which quadratically stabilizes the system for all admissible uncertainties. This state feedback control law consists of linear and nonlinear feedback control terms. The linear feedback control term is generalized from a well-known H_∞ result, while the nonlinear term can be viewed as a correcting term for the presence of nonlinear bounded uncertainty. This stabilization result is extended to static output feedback and to systems for which the nonlinear uncertainty satisfies generalized matching conditions. Furthermore, we point out that in the presence of nonlinear uncertainty the global quadratic stability may be destroyed by some arbitrary small mismatched uncertainty in the matrix, and proceed to establish the region of semi-global quadratic stability of the controlled system. © 1998 John Wiley & Sons, Ltd.     

Stability analysis of optimally quantised LFT-feedback systems

This article is concerned with the stability analysis of quantised feedback control systems which contain the optimal dynamic quantisers recently proposed by the authors. First, it is shown that a sort of separation property of quantiser-controller design holds as far as the feedback system stability concerns. This allows us to design feedback controllers independently of the choice of quantisers. Then, based on this property, a necessary and sufficient condition is derived for the optimally quantised feedback system to be stable, which is described in terms of the poles/zeros of a linear feedback system to be quantised. Finally, we provide a class of suboptimal dynamic quantisers for which the resulting quantised control systems are guaranteed to be stable.     

基于局部-整体反馈控制的多个体系统的稳定性

本文提出了一类基于局部-整体反馈控制的多个体系统稳定性问题的框架.该问题具有以下特点:1)每个个体有自身的动力学演化规律,本文假设他们为带噪声的线性回归离散动态方程;2)每个个体通过优化自身的局部目标函数与其他个体耦合在一起.在此框架下,本文给出了最优的局部-整体反馈控制律,并初步研究了在此控制律作用下系统的参数对闭环系统均方稳定性的影响.     

Stability analysis for nonlinear feedback control systems with linear actuators

Often, nonlinear feedback controllers are implemented with linear actuators, which have faster dynamics when compared with non-linear dynamics of the plant and controller models. However, how faster should the dynamics of the linear actuator be to ensure stability of the given nonlinear feedback control system? This note gives an analysis for the underlying stability issues and provides quantitative measures for the linear actuators employed in nonlinear feedback control systems.