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Quadratic stabilization for uncertain stochastic systems

控制理论与应用 , 2005,
Abstract: This paper discusses the robust quadratic stabilization control problem for stochastic uncertain systems,where the uncertain matrix is norm bounded,and the external disturbance is a stochastic process.Two kinds of controllers are designed,which include state feedback case and output feedback case.The conditions for the robust quadratic stabilization of stochastic uncertain systems are given via linear matrix inequalities.The detailed design methods are presented.Numerical examples show the effectiveness of our results.
New Condition of Stabilization of Uncertain Continuous Takagi-Sugeno Fuzzy System based on Fuzzy Lyapunov Function  [cached]
Yassine Manai,Mohamed Benrejeb
International Journal of Intelligent Systems and Applications , 2012,
Abstract: This paper deals with the stabilization of Takagi-Sugeno fuzzy models. Using non-quadratic Lyapunov function, new sufficient stabilization criteria with PDC controller are established in terms of Linear Matrix Inequality. Finally, a stabilization condition for uncertain system is given.
The Stabilization of Uncertain Symmetric Composite Systems

Yang Guanghong,Zhang Siying,

自动化学报 , 1995,
Abstract: This paper investigates the problem of quadratic stabilization for uncertain symmetric composite systems, Some sufficient conditions for quadratic stabilizability of these systems and a method of computing feedback control laws are given, the testing of the conditions and the computing of feedback control laws can be completed by solving the corresponding problem for two lowerorder systems.
Continuous higher-order sliding mode control for multi-input multi-output nonlinear uncertain system

控制理论与应用 , 2016, DOI: 10.7641/CTA.2016.50912
Abstract: 针对一类MIMO非线性不确定系统, 提出一种新的连续高阶滑模控制算法. 引入状态反馈使得系统高阶滑 模控制问题等效转换为多变量不确定积分链的有限时间稳定问题, 首先针对标称系统设计有限时间到达连续控制 律, 实现系统状态快速收敛, 然后采用多变量非解耦形式超螺旋算法克服系统不确定性, 实现鲁棒性, 最终使得系统 控制作用连续、滑模抖振得以大大抑制. 基于二次型Lyapunov函数证明系统的有限时间稳定性. 针对三阶不确定系 统有限时间稳定和气垫船圆形航迹跟踪问题分别进行了仿真, 验证了所提算法的有效性、鲁棒性.
This paper proposes a new continuous higher-order sliding mode control scheme for a class of MIMO nonlinear uncertain system. After implemented state feedback control, higher-order sliding mode control problem of the original uncertain nonlinear system is equivalently transformed into finite time stability problem of multivariable uncertain integror chains. A finite time continuous control law is firstly employed to guarantee rapid convergence of system states and finite time stabilization of nominal integral chain system, then multivariable non-coupling super-twisting algorithm is designed to overcome system uncertainties and achieve robustness. Finally, the whole control effect is continuous and high frequency chattering phenomenon of sliding mode is greatly weakened. Finite time stability of the closed loop system is proved strictly based on quadratic Lyapunov function. Examples concerning finite-time stabilization of a third order uncertain system and the hovercraft circular trajectory tracking are simulated respectively to verify the effectiveness and the robustness of the proposed approach.
Stabilization of uncertain systems using quantized and lossy observations and uncertain control inputs  [PDF]
Kunihisa Okano,Hideaki Ishii
Computer Science , 2015,
Abstract: In this paper, we consider a stabilization problem of an uncertain system in a networked control setting. Due to the network, the measurements are quantized to finite-bit signals and may be randomly lost in the communication. We study uncertain autoregressive systems whose state and input parameters vary within given intervals. We derive conditions for making the plant output to be mean square stable, characterizing limitations on data rate, packet loss probabilities, and magnitudes of uncertainty. It is shown that a specific class of nonuniform quantizers can achieve stability with a lower data rate compared with the common uniform one.

XU Shengyuan,YANG Chengwu,

自动化学报 , 2000,
Abstract: In this paper, the problems of robust stability and robust stabilization for uncertain generalized systems are considered. The concepts of 'generalized quadratic stability' and 'generalized quadratic stabilizability' for uncertain generalized systems are proposed. In terms of matrix inequalities, necessary and sufficient conditions under which the considered system is robustly stable and robustly stabilizable are derived respectively. Furthermore, the robust stabilizing state feedback control law can be designed by finding a solution to a given matrix inequality.
Robust stabilization of uncertain Lur''e-Postnikov systems with state delay

CHEN Wan-Yi,

控制理论与应用 , 2003,
Abstract: Using Lyapunov and a Razumikhin type method,robust stabilization of uncertain Lur'e Postnikov systems with delay state is discussed. For uncertain Lur'e Postnikov system with delay state and with some norm bounded perturbations, if its coefficient matrices satisfy an algebraic Riccati inequality, then via a linear static and/or dynamic state feedback, quadratic stability for its closed loop system is guaranteed. Also, using a Razumikhin type appraoch, a sufficient condition is given for the stabilization of a class of uncertain nonlinear systems with time varying delay.
Practical Stabilization of Counterfactual Quantum Cryptography  [PDF]
Musheng Jiang, Shihai Sun, Linmei Liang
Journal of Quantum Information Science (JQIS) , 2011, DOI: 10.4236/jqis.2011.13016
Abstract: A novel counterfactual quantum key distribution scheme was proposed by T.-G. Noh and a strict security analysis has been given by Z.-Q.Yin, in which two legitimate geographical separated couples may share secret keys even when the key carriers are not traveled in the quantum channel. However, there are still plenty of practical details in this protocol that haven’t been discussed yet, which are of significant importance in physical implementation. In this paper, we will give a practical analysis on such kind of counterfactual quantum cryptography in the aspects of quantum bit error rate (QBER) and stabilization. Furthermore, modified schemes are proposed, which can obtain lower QBER and will be much more robust on stabilization in physical implementation.
Output Feedback Stabilization of Linear Time-Varying Uncertain Delay Systems
Tomoaki Hashimoto,Takashi Amemiya
Mathematical Problems in Engineering , 2009, DOI: 10.1155/2009/457468
Abstract: This paper investigates the output feedback stabilization problem of linear time-varying uncertain delay systems with limited measurable state variables. Each uncertain parameter and each delay under consideration may take arbitrarily large values. In such a situation, the locations of uncertain entries in the system matrices play an important role. It has been shown that if a system has a particular configuration called a triangular configuration, then the system is stabilizable irrespective of the given bounds of uncertain variations. In the results so far obtained, the stabilization problem has been reduced to finding the proper variable transformation such that an -matrix stability criterion is satisfied. However, it still has not been shown whether the constructed variable transformation enables the system to satisfy the -matrix stability condition. The objective of this paper is to show a method that enables verification of whether the transformed system satisfies the -matrix stability condition.
Memoryless Robust Stabilization of a Class of Uncertain Linear Time-Delay Systems


自动化学报 , 1998,
Abstract: This paper presents a controller for robust stabilization of a class of uncertain linear dynamic systems with time-delays in both state and control. The uncertain systems under consideration are described by state differential equations which depend on time-varying unknown -but-bounded uncertain parameters, The sufficient conditions for quadratic stability of closed-loop systems are derived. The desired linear state feedback control law can be constructed by synthesis of an H~ standard problem of equivalent linear time-invariant systems, that is to say, the static controller gain can be obtained by solving an algebraic Riccati equation , and thus the existence and feasibility of solution can be ensured.
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