Necessary and Sufficient Conditions for the Passivicability of Linear Distributed Systems
Necessary and Sufficient Conditions for the Passivicability of Linear Distributed Systems
复制标题
线性分布式系统无源性的充要条件
DOI：
10.1023/a:1023230128592
复制
发表时间：
2003
影响因子：
0.7
通讯作者：
Alexander L. Fradkov
中科院分区：
文献类型：
--
作者：
V. A. Bondarko;Alexander L. Fradkov
众所周知，对于一类广泛的系统，超最小相位对于系统的严格被动性来说是必要且充分的。此类包含集中参数系统和分布式参数系统，包括描述热交换和扩散过程的抛物线方程。我们的结果适用于有限维输入和输出空间，这对于应用和覆盖具有不同数量的输入和输出的系统很重要，其中无源性被某些矩形矩阵 G 的 G-无源性取代。给出了直接包含控制的扩散型一维偏微分方程的示例。证明基于雅库博维奇-卡尔曼引理和内菲多夫-肖洛霍维奇指数稳定定理的无限维变体。
For a wide class of systems, as is known, hyper-minimal phase is necessary and sufficient for the strict passivicability of a system. This class contains both concentrated- and distributed-parameter systems, including parabolic equations that describe heat-exchange and diffusion processes. Our results are applicable to finite-dimensional input and output spaces, which are important for application and cover systems with different numbers of inputs and outputs for which passivity is superseded by the G-passivity of some rectangular matrix G. An example of a diffusion-type one-dimensional partial differential equation directly containing control is given. Proofs are based on the infinite-dimensional variant of the Yakubovich–Kalman lemma and Nefedov–Sholokhovich exponential stabilization theorem.