广义不确定系统的分步H ∞鲁棒控制

针对具有参数不确定性和外部未知扰动的广义系统鲁棒控制问题，在系统状态不可测时，提出一种基于广义函数观测器的分步H∞控制方法．首先确定使系统二次容许且具有一定干扰抑制度和不确定参数限制度的状态反馈控制器；然后构造广义函数观测器以实现反馈控制．结果证明．闭环系统可以保持二次容许．且H∞鲁棒性能可任意逼近原状态反馈系统．具体算例表明了该方法的有效性．     

Nonquadratic Lyapunov functions for robust stability analysis oflinear uncertain systems

In this note, we derive conditions of existence of a homogeneous polynomial Lyapunov function of an arbitrary even degree establishing global asymptotic stability of linear system with box-bounded uncertainty. Verification of these conditions is reduced to solving a convex minimization problem. We produce numerical examples that demonstrate significant improvement in estimates of admissible uncertainty bounds compared with estimates obtained via the most commonly used quadratic Lyapunov functions     

不确定广义系统动态输出反馈鲁棒H∞控制器设计

在E确定其他系数矩阵均存在不确定性情况下，基于线性矩阵不等式给出系统的动态输出反馈鲁棒H∞控制器设计方法，所得的控制律保证闭环系统对所有允许的不确定性是正则、稳定，无脉冲的且满足给定的H∞性能指标，算例说明了该控制器设计方法的有效性。     

Optimal control and robust stability of uncertain impulsive dynamical systems

This paper studies the problem of optimal feedback control and robust stability for uncertain impulsive dynamical systems. By using algebraic inequalities, Riccati and Hamilton‐Jacobi inequalities, the conditions are derived under which not only the uncertain impulsive dynamical system has robust asymptotic stability but also the value of the optimal hybrid performance functional can be estimated. An example is also given to illustrate our results. © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

不确定广义时滞系统的鲁棒稳定方法研究

研究一类带有时滞不确定广义系统的鲁棒渐近稳定问题．利用Lyapunov稳定性定理和线性矩阵不等式工具,得到了广义系统正则、鲁棒渐近稳定的时滞相关充分条件．为了降低所得结果的保守性,避免了采用系统模型变换和利用矩阵不等式方法．进一步,建立一个具有线性矩阵不等式约束的凸优化问题,利用Matlab软件中的LMI工具箱求解,得到保证广义系统鲁棒渐近稳定的最大可允许时滞上界．仿真示例表明了该方法的有效性．     

A descriptor system approach to robust stability of uncertain neutral systems with discrete and distributed delays

The robust stability of uncertain linear neutral systems with discrete and distributed delays is investigated. The uncertainties under consideration are norm bounded, and possibly time varying. The proposed stability criteria are formulated in the form of a linear matrix inequality and it is easy to check the robust stability of the considered systems. Numerical examples are given to indicate significant improvements over some existing results.     

不确定广义系统的弹性H∞控制

研究了具有范数有界不确定性的广义系统的弹性H_∞控制问题. 首先证明了广义系统的有界实引理可以用一个严格的线性矩阵不等式来描述. 在此基础上, 针对控制器存在加性摄动的情形, 以严格线性矩阵不等式约束条件给出了弹性H_∞状态反馈控制器存在的充分必要条件, 并给出了控制器的显式表示. 算例验证了本文方法的可行性.     

Lyapunov stability theory of nonsmooth systems

This paper develops nonsmooth Lyapunov stability theory and LaSalle's invariance principle for a class of nonsmooth Lipschitz continuous Lyapunov functions and absolutely continuous state trajectories. Computable tests based on Filipov's differential inclusion and Clarke's generalized gradient are derived. The primary use of these results is in analyzing the stability of equilibria of differential equations with discontinuous right-hand side such as in nonsmooth dynamic systems or variable structure control     

Delay-independent robust stability of uncertain linear systems

In this paper we present some new sufficient conditions for robust stability of linear systems with uncertain time delay as well as structured parameter uncertainty. The stability robustness bounds obtained from the new sufficient conditions are independent of the size of time delay. Some illustrative examples are given.     

A Lyapunov functional approach to robust stability analysis of continuous-time uncertain linear systems in polytopic domains

In this paper, a sufficient linear matrix inequality (LMI) condition is presented for robust stability analysis of continuous-time linear time-invariant (LTI) systems in polytopic domains. The underlying idea behind the proposed approach is to introduce a family of complex functions which map the closed right-hand side of the complex plane into the inside of the closed unit circle centered at the origin. Then, the mapping properties are used to assure that all the eigenvalues of a system are located in the open left-hand side of the complex plane. Examples show the validity of the proposed condition.     

Delay-dependent robust stability of uncertain networked control systems with multiple state time-delays

In this paper, delay-dependent robust stability for a class of uncertain networked control systems （NCSs） with multiple state time-delays is investigated. Modeling of multi-input and multi-output （MIMO） NCSs with networkinduced delays and uncertainties through new methods are proposed. Some new stability criteria in terms of LMIs are derived by using Lyapunov stability theory combined with linear matrix inequalities （LMIs） techniques. We analyze the delay-dependent asymptotic stability and obtain maximum allowable delay bound （MADB） for the NCSs with the proposed methods. Compared with the reported results, the proposed results obtain a much less conservative MADB which are more general. Numerical example and simulation is used to illustrate the effectiveness of the proposed methods.     

不确定多通道奇异大系统分散鲁棒H∞控制

研究不确定多通道奇异系统的鲁棒分散H_∞控制问题,假定不确定性是时不变、范数有界,且存在于系统和控制输入矩阵中．主要考虑分散H_∞输出反馈控制问题．推导出了使不确定多通道奇异系统能鲁棒稳定且满足一定的性能指标的充分必要条件,没有等式约束的非线性矩阵不等式条件,采用两步同伦法迭代来求解非线性矩阵不等式(NMI),首先,通过逐步对控制器的系数矩阵加上结构限制,计算出当确定性不存在时的标称系统的分散H_∞控制器．然后,逐步改变标称系统分散控制器的系数,计算出不确定性参数存在时的分散鲁棒控制器．在每一阶段,每一次迭代过程中,通过交替固定NMI的一个变量,使NMI转变为线性矩阵不等式(LMI)．数值例子说明了本文提出的方法的有效性．