Strict Lyapunov(严格的李雅普诺夫)研究综述
Strict Lyapunov 严格的李雅普诺夫 - In this note, we use the Mazenc construction to design a simple strict Lyapunov function in a rather intuitive manner, based on a first-choice function whose derivative is negative semidefinite. [1] In the stability analysis, a strict Lyapunov function and its conditions are studied to prove asymptotic stability for second-order systems and Lagrangian systems. [2] Two illustrative examples illustrate that the proposed scheme can be used to ensure UGES even though finding a common quadratic strict Lyapunov function is sometimes impossible for arbitrarily switched LTI systems. [3] The finite-time stability of the closed-loop attitude control system is proved by using a continuously-differentiable, homogeneous and strict Lyapunov function. [4] First, a strict Lyapunov function is proposed for this dynamics and the conditions of strict passivity with a corresponding output are given. [5] Using the strict Lyapunov function, some sufficient conditions in terms of matrix inequalities are obtained for the boundary ISS of the closed-loop hyperbolic PDE-ODE systems. [6] Strict Lyapunov functions for these systems are provided. [7] Finally, strict Lyapunov analysis is provided to show the globally finite-time stability of the closed-loop sliding mode system and an application to Buck converter is presented. [8] For a linear parameterization of the unknown parameters, a new strict Lyapunov function construction method is first presented for I&I adaptive control systems using the notion of integral inputto-state stability (iISS). [9] More significantly, for the first time in the literature, a strict Lyapunov function is provided and uniform global asymptotic stability for the closed-loop system is established. [10] For this new architecture we first prove a stability and performance analysis test, based on certain strict Lyapunov conditions, and show that these reduce to LMIs when using quadratic Lyapunov certificates. [11] For a realistic structure preserving power system with voltage dependent loads, we propose a sufficient condition based on a strict Lyapunov energy function, which is utilized to design a nonlinear adaptive SVC controller. [12] This paper proposes strict Lyapunov functions (SLFs) for the Saturated-Proportional-Saturated-Derivative with gravity cancellation controller for the case when the robot manipulator has non-ideal actuators and without taking into account the viscous friction in the model. [13] When a nonlinear system has a strict Lyapunov function, its stability can be studied using standard tools from Lyapunov stability theory. [14] Asymptotic stability of the closed loop system is proven using a Strict Lyapunov Function. [15]在这篇笔记中，我们使用 Mazenc 构造以一种相当直观的方式设计了一个简单的严格 Lyapunov 函数，该函数基于导数为半负定的首选函数。 [1] 在稳定性分析中，研究了严格的李雅普诺夫函数及其条件，以证明二阶系统和拉格朗日系统的渐近稳定性。 [2] 两个说明性示例说明了所提出的方案可用于确保 UGES，即使对于任意切换的 LTI 系统有时不可能找到共同的二次严格 Lyapunov 函数。 [3] 采用连续可微、齐次、严格的Lyapunov函数证明了闭环姿态控制系统的有限时间稳定性。 [4] 首先，针对这种动力学提出了严格的 Lyapunov 函数，并给出了具有相应输出的严格无源性条件。 [5] 利用严格的Lyapunov函数，得到了闭环双曲PDE-ODE系统边界ISS的一些矩阵不等式的充分条件。 [6] 为这些系统提供了严格的 Lyapunov 函数。 [7] 最后，提供了严格的李雅普诺夫分析，以展示闭环滑模系统的全局有限时间稳定性，并提出了在降压转换器中的应用。 [8] 对于未知参数的线性参数化，首先为 I&I 自适应控制系统提出了一种新的严格 Lyapunov 函数构造方法，该方法使用积分输入状态稳定性 (iISS) 的概念。 [9] 更重要的是，文献中首次提供了严格的 Lyapunov 函数，并为闭环系统建立了统一的全局渐近稳定性。 [10] 对于这个新架构，我们首先证明了基于某些严格的 Lyapunov 条件的稳定性和性能分析测试，并表明当使用二次 Lyapunov 证书时，这些测试可以简化为 LMI。 [11] 对于具有电压相关负载的现实结构保持电力系统，我们提出了基于严格 Lyapunov 能量函数的充分条件，用于设计非线性自适应 SVC 控制器。 [12] 本文针对具有重力消除控制器的饱和比例饱和导数提出了严格的 Lyapunov 函数 (SLF)，用于机器人机械臂具有非理想执行器且不考虑模型中的粘性摩擦的情况。 [13] 当非线性系统具有严格的 Lyapunov 函数时，可以使用 Lyapunov 稳定性理论中的标准工具来研究其稳定性。 [14] 闭环系统的渐近稳定性是使用严格李雅普诺夫函数证明的。 [15]
strict lyapunov function 严格的李雅普诺夫函数
In this note, we use the Mazenc construction to design a simple strict Lyapunov function in a rather intuitive manner, based on a first-choice function whose derivative is negative semidefinite. [1] In the stability analysis, a strict Lyapunov function and its conditions are studied to prove asymptotic stability for second-order systems and Lagrangian systems. [2] Two illustrative examples illustrate that the proposed scheme can be used to ensure UGES even though finding a common quadratic strict Lyapunov function is sometimes impossible for arbitrarily switched LTI systems. [3] The finite-time stability of the closed-loop attitude control system is proved by using a continuously-differentiable, homogeneous and strict Lyapunov function. [4] First, a strict Lyapunov function is proposed for this dynamics and the conditions of strict passivity with a corresponding output are given. [5] Using the strict Lyapunov function, some sufficient conditions in terms of matrix inequalities are obtained for the boundary ISS of the closed-loop hyperbolic PDE-ODE systems. [6] Strict Lyapunov functions for these systems are provided. [7] For a linear parameterization of the unknown parameters, a new strict Lyapunov function construction method is first presented for I&I adaptive control systems using the notion of integral inputto-state stability (iISS). [8] More significantly, for the first time in the literature, a strict Lyapunov function is provided and uniform global asymptotic stability for the closed-loop system is established. [9] This paper proposes strict Lyapunov functions (SLFs) for the Saturated-Proportional-Saturated-Derivative with gravity cancellation controller for the case when the robot manipulator has non-ideal actuators and without taking into account the viscous friction in the model. [10] When a nonlinear system has a strict Lyapunov function, its stability can be studied using standard tools from Lyapunov stability theory. [11] Asymptotic stability of the closed loop system is proven using a Strict Lyapunov Function. [12]在这篇笔记中，我们使用 Mazenc 构造以一种相当直观的方式设计了一个简单的严格 Lyapunov 函数，该函数基于导数为半负定的首选函数。 [1] 在稳定性分析中，研究了严格的李雅普诺夫函数及其条件，以证明二阶系统和拉格朗日系统的渐近稳定性。 [2] 两个说明性示例说明了所提出的方案可用于确保 UGES，即使对于任意切换的 LTI 系统有时不可能找到共同的二次严格 Lyapunov 函数。 [3] 采用连续可微、齐次、严格的Lyapunov函数证明了闭环姿态控制系统的有限时间稳定性。 [4] 首先，针对这种动力学提出了严格的 Lyapunov 函数，并给出了具有相应输出的严格无源性条件。 [5] 利用严格的Lyapunov函数，得到了闭环双曲PDE-ODE系统边界ISS的一些矩阵不等式的充分条件。 [6] 为这些系统提供了严格的 Lyapunov 函数。 [7] 对于未知参数的线性参数化，首先为 I&I 自适应控制系统提出了一种新的严格 Lyapunov 函数构造方法，该方法使用积分输入状态稳定性 (iISS) 的概念。 [8] 更重要的是，文献中首次提供了严格的 Lyapunov 函数，并为闭环系统建立了统一的全局渐近稳定性。 [9] 本文针对具有重力消除控制器的饱和比例饱和导数提出了严格的 Lyapunov 函数 (SLF)，用于机器人机械臂具有非理想执行器且不考虑模型中的粘性摩擦的情况。 [10] 当非线性系统具有严格的 Lyapunov 函数时，可以使用 Lyapunov 稳定性理论中的标准工具来研究其稳定性。 [11] 闭环系统的渐近稳定性是使用严格李雅普诺夫函数证明的。 [12]