线性定常时滞系统的鲁棒控制

在建立线性定常时滞系统模型的基础上,给出了时滞系统是独立鲁棒稳定的条件,并利用Lyapunov理论给予一些定理的证明,同时设计出了使闭环系统时滞独立鲁棒稳定的状态反馈控制器（即时滞独立鲁棒镇定问题）,最后给出的一个数值例子中用Matlab编程求出了符合条件的正定矩阵和控制律,从算例结果验证了所得出的结论。     

一类非线性时滞大系统的自适应鲁棒控制

研究一类包含参数不确定性和关联时滞的不确定时滞组合大系统的鲁棒控制问题。利用线性矩阵不等式技术和自适应参数估计方法，设计鲁棒自适应控制器，从而保证闭环系统渐近稳定。最后给出了仿真示例，说明了该方法的有效性。     

不确定时滞混沌系统的鲁棒控制

针对不确定时滞混沌系统中不稳定不动点的控制需要，应用线性矩阵不等式（LMI）方法，得到了系统存在时滞反馈控制器的充分条件，并利用该控制器对系统中存在的不稳定周期轨道的跟踪问题进行研究。数值仿真结果表明了该方法的有效性。     

海运船舶电力推进系统的鲁棒控制

针对海运船舶电力推进系统的数学模型,采用鲁棒控制方法设计状态反馈控制器。主要是基于李雅普诺夫稳定性理论,推导使系统稳定且满足 H￥性能的控制器存在的条件,利用 MATLAB软件进行仿真求解扰动抑制度γ,并获得相应的单位阶跃响应曲线,表明用鲁棒控制方法对海运船舶电力系统进行控制是可行的。     

一类非仿射系统的鲁棒控制

考虑汽车转向控制中出现的微分包含系统的控制问题。首先用一非仿射不确定系统来描述这一微分包含系统，基于耗散理论分析了这一类非仿射不确定系统的鲁棒控制问题。并针对该非线性系统的有界性，给定系统鲁棒稳定的充分条件是满足一线性矩阵不等式，最后给出了一个仿真计算实例以验证算法的有效性。     

应用LM I设计鲁棒严格正实传递函数

讨论稳定的实区间多项式族是否存在一个实多项式使之严格正实化问题。通过线性矩阵不等式给出了存在此项式的充要条件,并利用Ｍａｔｌａｂ中的ＬＭＩ软件包求解满足条件的不变多项式。具体算例说明了该算法的有效性。     

广义系统输出反馈严格正实控制器设计

研究连续广义系统的正实控制问题。目的是设计静态输出反馈和动态输出反馈严格正实控制器使得闭环系统容许且扩展严格正实。基于广义系统严格正实引理，利用线性矩阵不等式和广义代数Riccati不等式，给出了广义系统静态输出反馈和动态输出反馈严格正实控制器存在的充要条件及设计方法。对动态输出反馈情形，给出了一个数值算例说明控制器设计方法的有效性及可行性。     

奇异摄动系统的鲁棒控制与仿真研究

研究参数不确定奇异摄动系统的状态反馈镇定问题,得到基于线性矩阵不等式（LMI）的系统状态反馈可镇定的充分条件,给出状态反馈控制器的设计算法。算例验证了该方法的可行性与有效性。而且,这种方法同时适用于标准奇异摄动系统和非标准奇异摄动系统的控制。最后通过例子进行了详细的仿真研究。     

参数和时延不确定性离散时间系统的 H∞鲁棒控制

针对含有参数和时延不确定性线性离散时间系统的鲁棒控制问题，构造改进的Lyapunov函数，并采用LMI与H∞鲁棒控制相结合的方法，使得系统在不含外界未知扰动时，只得满足一个矩阵不等式，便可通过状态的静态反馈控制使闭环系统达到二次稳定；而在系统含有外界未知扰动时，结合基于离散时间系统的无源性控制方法，同样只得满足一个矩阵不等式，便可通过状态的静态反馈控制使得闭环系统达到理想的干扰抑制作用。     

不确定系统具有圆盘区域极点约束的鲁棒控制

对一类不确定线性系统,提出了存在状态反馈控制律,使得闭环系统的所有极点均位 于一给定圆盘中的一个充分必要条件.结合控制律反馈增益参数极小化的要求,建立了一个具 有线性矩阵不等式约束的凸优化问题,通过该问题的解,可以构造一个具有较小反馈增益参数 和给定要求的控制律.所提出的方法既可应用到连续系统,也可应用到离散系统.     

Robust observer-based control for uncertain discrete-time piecewise affine systems

The main contribution of this paper is to present a novel robust observer-based controller design method for discrete-time piecewise affine systems with norm-bounded uncertainties.The key ideas are to ...     

New characterization of positive realness and control of a class of uncertain polytopic discrete-time systems

This paper deals with the problems of positive real analysis and control synthesis for a class of discrete-time polytopic systems with uncertainties. The systems under consideration are modelled in a polytopic form with linear fractional uncertainties in its vertices. A new linear matrix inequality (LMI) characterization of positive realness for this class of systems is given. It enables one to check the positive realness by using parameter-dependent Lyapunov function. This new characterization exhibits a kind of decoupling between the Lyapunov matrix and the system matrices, which is subsequently exploited for control design. Based on the new result, sufficient conditions with reduced conservatism are obtained. A numerical example is also included to demonstrate the applicability of the proposed results.     

Robust reliability method for non-fragile guaranteed cost control of parametric uncertain systems

The problem of non-fragile guaranteed cost control of uncertain systems is studied from a new point of view of reliability against uncertainties. An efficient robust reliability method for the analysis and design of non-fragile guaranteed cost controller of parametric uncertain systems is presented systematically. By the method, a robust reliability measure of an uncertain control system satisfying required robust performance can be obtained, and the robustness bounds of uncertain parameters such that the control cost of a system is guaranteed can be provided. The optimal non-fragile guaranteed cost controller obtained in the paper may possess optimal guaranteed cost performance satisfying the precondition that the system is robustly reliable with respect to uncertainties occurring in both the controlled plant and controller gain. The presented formulations are in the framework of linear matrix inequality and thus can be carried out conveniently. The presented method provides an essential basis for the tradeoff between reliability and control cost in controller design of uncertain systems. Two numerical examples are provided to demonstrate the efficiency and feasibility of the presented method. It is shown that the coordination and simultaneous realization of the system performance, control cost, and robust reliability in control design of uncertain systems are significant.     

一类基于观测器的网络控制系统鲁棒控制器设计

研究一类基于状态观测器的网络控制系统鲁棒稳定性和鲁棒控制器设计问题.考虑传感器时钟驱动、控制器和执行器事件驱动以及小于等于一个采样周期的不确定时延,建立了基于状态观测器的网络控制系统增广模型.利用线性矩阵不等式方法推导出该系统鲁棒稳定的条件,进一步给出了鲁棒控制律和状态观测器设计方法.数值仿真算例证明了分析方法和结果的有效性.     

Robust stabilization for a class of nonlinear networked control systems

The problem of robust stabilization for a class of uncertain networked control systems （NCSs） with nonlinearities satisfying a given sector condition is investigated in this paper. By introducing a new model of NCSs with parameter uncertainty, network-induced delay, nonlinearity and data packet dropout in the transmission, a strict linear matrix inequality （LMI） criterion is proposed for robust stabilization of the uncertain nonlinear NCSs based on the Lyapunov stability theory. The maximum allowable transfer interval （MATI） can be derived by solving the feasibility problem of the corresponding LMI. Some numerical examples are provided to demonstrate the applicability of the proposed algorithm.     

Robust model predictive control for continuous uncertain systems with state delay

This paper is concerned with robust model predictive control for linear continuous uncertain systems with state delay and control constraints. A piecewise constant control sequence is calculated by minimizing the upper-bound of the infinite horizon quadratic cost function. At each sampling time, the sufficient conditions for the existence of the model predictive control are derived, and expressed as a set of linear matrix inequalities. The robust stability of the closed-loop systems is guaranteed by the proposed design method. A numerical example is given to illustrate the main results.     

Robust model predictive control for continuous uncertain systems with state delay

This paper is concerned with robust model predictive control for linear continuous uncertain systems with state delay and control constraints, A piecewise constant control sequence is calculated by minimizing the upper-bound of the infinite horizon quadratic cost function, At each sampling time, the sufficient conditions for the existence of the model predictive control are derived, and expressed as a set of linear matrix inequalities. The robust stability of the closed-loop svstems is guaranteed bv the proposed design method. A numerical example is given to illustrate the main results.     

Robust synchronization of fractional-order unified chaotic systems via linear control

A new scheme for accomplishing synchronization between two fractional-order unified chaotic systems is proposed in this paper. The scheme does not require that the nonlinear dynamics of the synchronization error system must be eliminated. Moreover, the parameter of the systems does not have to be known. A controller is a linear feedback controller, which is simple in implementation. It is designed based on an LMI condition. The LMI condition guarantees that the synchronization between the slave system and the master system is achieved. Numerical simulations are performed to demonstrate the effectiveness of the proposed scheme.     

Robust energy-to-peak filter design for stochastic time-delay systems

This paper considers the robust energy-to-peak filtering problem for uncertain stochastic time-delay systems. The stochastic uncertainties appear in both the dynamic and the measurement equations and the state delay is assumed to be time-varying. Attention is focused on the design of full-order and reduced-order filters guaranteeing a prescribed energy-to-peak performance for the filtering error system. Sufficient conditions are formulated in terms of linear matrix inequalities (LMIs), and the corresponding filter design is cast into a convex optimization problem which can be efficiently handled by using standard numerical algorithms. In addition, the results obtained are further extended to more general cases where the system matrices also contain uncertain parameters. The most frequently used ways of dealing with parameter uncertainties, including polytopic and norm-bounded characterizations, have been taken into consideration, with convex optimization problems obtained for the design of desired robust energy-to-peak filters.