A Generalized LMI Formulation for Input-Output Analysis of Linear Systems of ODEs Coupled with PDEs
A Generalized LMI Formulation for Input-Output Analysis of Linear Systems of ODEs Coupled with PDEs
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DOI：
10.1109/cdc40024.2019.9030224
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发表时间：
2019-04
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影响因子：
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通讯作者：
Sachin Shivakumar;Amritam Das;S. Weiland;M. Peet
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文献类型：
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作者：
Sachin Shivakumar;Amritam Das;S. Weiland;M. Peet
本文研究了有限区域上偏微分方程与常微分方程耦合的线性系统的输入输出性质。本文利用最近发展起来的基本状态概念和相应的无边界条件表示，将常微分方程的KYP引理的充分性证明推广到耦合常微分方程-偏微分方程系统.广义KYP的条件进行了测试，使用一个正矩阵参数化的有界算子，从而在一个有限维的LMI，其可行性意味着初步证明的无源性或L2增益的系统。在任何一步都不涉及离散化或近似，定理中没有保守性。与其他计算方法的比较表明，得到的界限是不保守的，在任何重要的意义上，计算复杂性低于现有的方法，涉及有限维投影的偏微分方程。
In this paper, we consider input-output properties of linear systems consisting of PDEs on a finite domain coupled with ODEs through the boundary conditions of the PDE. This work generalizes the sufficiency proof of the KYP Lemma for ODEs to coupled ODE-PDE systems using a recently developed concept of fundamental state and the associated boundary-condition-free representation. The conditions of the generalized KYP are tested using a positive matrix parameterization of bounded operators resulting in a finite-dimensional LMI, the feasibility of which implies prima facie provable passivity or L2-gain of the system. No discretization or approximation is involved at any step and there is no conservatism in the theorems. Comparison with other computational methods show that bounds obtained are not conservative in any significant sense and that computational complexity is lower than existing methods involving finite-dimensional projection of PDEs.