Stability and quadratic Lyapunov functions for nD systems
Stability and quadratic Lyapunov functions for nD systems
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nD 系统的稳定性和二次 Lyapunov 函数
DOI：
10.1109/nds.2007.4509541
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
Jan C. Willems
中科院分区：
文献类型：
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作者：
Jan C. Willems
本文讨论了由线性常系数偏微分方程描述的nD系统的稳定性的一些观点和初步结果。所用的稳定性概念是LQ 2-稳定性和LQ 2-渐近稳定性，以时间作为一个区别变量。对于标量方程，推导了稳定性条件，包括将这些条件转化为系统参数的线性矩阵不等式的方法。这些条件被解释为涉及许多独立变量的系统的李雅普诺夫函数。多变量nD系统的几个公开问题制定。
We discuss some ideas and preliminary results on the stability of nD systems described by linear constant coefficient PDE's. The stability concept used is Lscr2-stability and Lscr2-asymptotic stability, with time as a distinguished variable. For scalar equations, stability conditions are derived, including methods to make these conditions into LMI's in the system parameters. These conditions are interpreted in terms of Lyapunov functions for systems involving many independent variables. Several open problems for multivariable nD systems are formulated.