In this paper, we propose a two-stage algorithm utilizing the Cauchy integral and the matrix-valued adaptive Fourier decomposition (abbreviated as matrix AFD) to identify transfer functions of linear time-invariant (LTI) multi-input multi-output (MIMO) systems in the continuous time case. In recent work of Alpay et al. (2017), a theory of adaptive rational approximation to matrix-valued Hardy space functions on the unit disk was established. The matrix-valued function theory has great potential in applications, in views of the practice of its scalar-valued counterparts. The algorithm and application aspects of the mentioned theory of Alpay et al. (2017) have not been developed. The theory was only written for the unit disk case corresponding to the discrete time systems. The contributions of the present paper are 3-fold. First, we construct an analogous adaptive approximation theory for complex matrix-valued Hardy space functions defined on a half of the complex plane, corresponding to the Laplace transforms of signals of finite energy whose Fourier transforms are supported on a half of the frequency domain. The half plane model corresponds to signals defined in the whole axis range which is an alternative case to signals defined in a compact interval. The second fold contribution lays on maximal selection of the pair $(a,P)$ where $a$ is a point of the right-half plane and $P$ is an orthogonal projection. We show that the optimal selection of $P$ is dependent on $a$ when $a$ is first fixed, that is $P=P\left(a\right)$, where $P:a\to P\left(a\right)$ has an explicit corresponding relation. Due to this relation we reduce the maximal selection of the pair $(a,P)$ to only that of the parameter $a$. This result can be extended to the compact intervals case as well. The third fold is, with the precise rule from $a$ to $P\left(a\right)$, we develop a practical algorithm for the adaptive approximation to the transfer function. Through an example we show that the proposed algorithm is effective in both the noise-free and noisy cases.

在本文中，我们提出了一种利用柯西积分和矩阵值自适应傅里叶分解（缩写为矩阵 AFD）的两阶段算法来识别线性时不变 (LTI) 多输入多输出 (MIMO) 的传递函数连续时间情况下的系统。在 Alpay 等人最近的工作中。(2017), 建立了单位圆盘上矩阵值哈代空间函数的自适应有理逼近理论。鉴于其标量值函数理论的实践，矩阵值函数理论具有巨大的应用潜力。Alpay等人提到的理论的算法和应用方面。(2017) 尚未开发。该理论只针对离散时间系统对应的单位盘情况而写. 本论文的贡献有 3 个方面。首先，我们为在复平面的一半上定义的复矩阵值哈代空间函数构建了一个类似的自适应逼近理论，对应于有限能量信号的拉普拉斯变换，其傅立叶变换在频域的一半上得到支持。半平面模型对应于在整个轴范围内定义的信号，这是在紧凑间隔中定义的信号的另一种情况。第二个折叠贡献在于对的最大选择$(\mathrm{一种},磷)$ 在哪里 $\mathrm{一种}$ 是右半平面的一个点并且 $磷$是正交投影。我们证明了最佳选择$磷$ 依赖于 $\mathrm{一种}$ 什么时候 $\mathrm{一种}$ 首先是固定的，即 $磷=磷\left(\mathrm{一种}\right)$， 在哪里 $磷：\mathrm{一种}\to 磷\left(\mathrm{一种}\right)$有明确的对应关系。由于这种关系，我们减少了对的最大选择$(\mathrm{一种},磷)$ 只有参数的那个 $\mathrm{一种}$. 这个结果也可以扩展到紧凑区间的情况。第三个折叠是，精确的规则来自$\mathrm{一种}$ 到 $磷\left(\mathrm{一种}\right)$，我们开发了一种实用的算法来自适应逼近传递函数。通过一个例子，我们表明所提出的算法在无噪声和有噪声的情况下都是有效的。