Nonquadratic Lyapunov functions for robust stability analysis of linear uncertain systems

Zelentsovsky A.L.

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Nonquadratic Lyapunov functions for robust stability analysis of linear uncertain systems

机译：非二次李雅普诺夫函数用于线性不确定系统的鲁棒稳定性分析

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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.

机译：在本说明中，我们推导了建立具有线性有限边界的线性系统的全局渐近稳定性的任意偶数阶齐次多项式Lyapunov函数的存在条件。这些条件的验证被简化为解决凸最小化问题。我们提供的数值示例表明，与通过最常用的二次Lyapunov函数获得的估计值相比，可允许不确定性范围的估计值有了显着改善。

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《IEEE Transactions on Automatic Control》 |1994年第1期|P.135-138|共4页
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Zelentsovsky A.L.;
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1. Nonquadratic Lyapunov functions for robust stability analysis oflinear uncertain systems [J] . Zelentsovsky A.L. IEEE Transactions on Automatic Control . 1994,第1期

机译：非二次Lyapunov函数用于线性不确定系统的鲁棒稳定性分析
2. A team algorithm for robust stability analysis and control design of uncertain time-varying linear systems using piecewise quadratic Lyapunov functions [J] . Almeida HLS., Falcao DM., Kaszkurewicz E., International Journal of Robust and Nonlinear Control . 2001,第4期

机译：基于分段二次Lyapunov函数的不确定时变线性系统鲁棒稳定性分析和控制设计的团队算法
3. A Lyapunov Functional Approach to Robust Stability Analysis of Continuous-Time Uncertain Linear Systems in Polytopic Domains [J] . Dong Hwan Lee, Myung Hwan Tak, Young Hoon Joo International Journal of Control, Automation, and Systems . 2013,第3期

机译：多域域连续时间不确定线性系统鲁棒稳定性分析的Lyapunov函数方法
4. A team algorithm for robust stability analysis and control design of uncertain time-varying linear systems using piecewise quadratic Lyapunov functions [C] . Almeida, H.L.S., Bhaya, . 1998

机译：基于分段二次Lyapunov函数的不确定时变线性系统鲁棒稳定性分析和控制设计的团队算法
5. Parameter-dependent Lyapunov functions and stability analysis of linear parameter-dependent dynamical systems. [D] . Zhang, Xiping. 2003

机译：依赖参数的Lyapunov函数和线性依赖参数的动力系统的稳定性分析。
6. Stability criteria on delay-dependent robust stability for uncertain neutral stochastic nonlinear systems with time-delay [O] . Tengyu Ma, Longsuo Li -1

机译：具有时滞的不确定中立随机非线性系统的时滞相关鲁棒稳定性的稳定性判据
7. Robust Stability Criteria for T-S Fuzzy Systems with Time-Varying Delays via Nonquadratic Lyapunov-Krasovskii Functional Approach [O] . Sung Hyun Kim 2016

机译：通过不规度Lyapunov-Krasovskii功能方法具有时变延迟的T-S模糊系统的稳健稳定性标准
8. Nonlinear System Analysis and Synthesis. Part I. Study of Lyapunov Functions for Problems of Control and of Optimality of Linear Systems [R] . Kalman, R. E., Szego, G. P., Englar, T. S. 1964

机译：非线性系统分析与综合。第一部分线性系统控制和最优性问题的Lyapunov函数研究

Nonquadratic Lyapunov functions for robust stability analysis of linear uncertain systems

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