数学代写|matlab代写|CONTINUOUS LINEAR SYSTEMS AND THEIR SOLUTIONS

matlab是一个编程和数值计算平台，被数百万工程师和科学家用来分析数据、开发算法和创建模型。

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等楖率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

数学代写|matlab代写|Input-Output Models of Linear Dynamic Systems

The block diagram in Figure $2.1$ represents a linear continuous system with three types of variables:

• Inputs, which are under our control, and therefore known to us, or at least measurable by us. (In the next chapter, however, they will be assumed to be known only statistically. That is, individual samples of $u$ are random but with known statistical properties.)
• State variables, which were described in the previous section. In most applications, these are “hidden variables,” in the sense that they cannot generally be measured directly but must be somehow inferred from what can be measured.
• Outputs, which are those things that can be known through measurements.
These concepts are discussed in greater detail in the following subsections.

数学代写|matlab代写|Dynamic Coefficient Matrices and Input Coupling Matrices

The dynamics of linear systems are represented by a set of $n$ first-order linear differential equations expressible in vector form as
\begin{aligned} \dot{x}(t) &=\frac{d}{d t} x(t) \ &=F(t) x(t)+C(t) u(t) \end{aligned}
where the elements and components of the matrices and vectors can be functions of time:
\begin{aligned} F(t)=& {\left[\begin{array}{ccccc} f_{11}(t) & f_{12}(t) & f_{13}(t) & \cdots & f_{1 n}(t) \ f_{21}(t) & f_{22}(t) & f_{23}(t) & \cdots & f_{2 n}(t) \ f_{31}(t) & f_{32}(t) & f_{33}(t) & \cdots & f_{3 n}(t) \ \vdots & \vdots & \vdots & \ddots & \vdots \ f_{n 1}(t) & f_{n 2}(t) & f_{n 3}(t) & \cdots & f_{n n}(t) \end{array}\right] } \ C(t)=& {\left[\begin{array}{ccccc} c_{11}(t) & c_{12}(t) & c_{13}(t) & \cdots & c_{1 r}(t) \ c_{21}(t) & c_{22}(t) & c_{23}(t) & \cdots & c_{2 r}(t) \ c_{31}(t) & c_{32}(t) & c_{33}(t) & \cdots & c_{3 r}(t) \ \vdots & \vdots & \vdots & \ddots & \vdots \ c_{n 1}(t) & c_{n 2}(t) & c_{n 3}(t) & \cdots & c_{n r}(t) \end{array}\right] } \ u(t)=& {\left[\begin{array}{lllll} u_{1}(t) & u_{2}(t) & u_{3}(t) & \cdots & u_{r}(t) \end{array}\right]^{\mathrm{T}} } \end{aligned}
The matrix $F(t)$ is called the dynamic coefficient matrix, or simply the dynamic matrix. Its elements are called the dynamic coefficients. The matrix $C(t)$ is called the input coupling matrix, and its elements are called input coupling coefficients. The $r$-vector $u$ is called the input vector.

数学代写|matlab代写|Difference Equations and State Transition Matrices

Difference equations are the discrete-time versions of differential equations. They are usually written in terms of forward differences $x\left(t_{k+1}\right)-x\left(t_{k}\right)$ of the state variable (the dependent variable), expressed as a function $\psi$ of all independent variables or of the forward value $x\left(t_{k+1}\right)$ as a function $\phi$ of all independent variables (including the previous value as an independent variable):
$$x\left(t_{k+1}\right)-x\left(t_{k}\right)=\psi\left(t_{k}, x\left(t_{k}\right), u\left(t_{k}\right)\right)$$
or
$$\begin{gathered} x\left(t_{k+1}\right)=\phi\left(t_{k}, x\left(t_{k}\right), u\left(t_{k}\right)\right), \ \phi\left(t_{k}, x\left(t_{k}\right), u\left(t_{k}\right)\right)=x\left(t_{k}\right)+\psi\left(t_{k}, x\left(t_{k}\right), u\left(t_{k}\right)\right) . \end{gathered}$$
The second of these (Equation 2.10) has the same general form of the recursive relation shown in Equation $2.4$, which is the one that is usually implemented for discrete-time systems.

For linear dynamic systems, the functional dependence of $x\left(t_{k+1}\right)$ on $x\left(t_{k}\right)$ and $u\left(t_{k}\right)$ can be represented by matrices:
\begin{aligned} x\left(t_{k+1}\right)-x\left(t_{k}\right) &=\Psi\left(t_{k}\right) x\left(t_{k}\right)+C\left(t_{k}\right) u\left(t_{k}\right), \ x_{k+1} &=\Phi_{k} x_{k}+C_{k} u_{k}, \ \Phi_{k} &=I+\Psi\left(t_{k}\right), \end{aligned}
where the matrices $\Psi$ and $\Phi$ replace the functions $\psi$ and $\phi$, respectively. The matrix $\Phi$ is called the state transition matrix $(S T M)$. The matrix $c$ is called the discrete-time input coupling matrix, or simply the input coupling matrix – if the discrete-time context is already established.

数学代写|matlab代写|Input-Output Models of Linear Dynamic Systems

• 输入，在我们的控制之下，因此我们知道，或者至少我们可以测量。（然而，在下一章中，将假定它们仅在统计上已知。也就是说，在是随机的，但具有已知的统计特性。）
• 状态变量，在上一节中进行了描述。在大多数应用程序中，这些是“隐藏变量”，因为它们通常不能直接测量，但必须以某种方式从可以测量的内容中推断出来。
• 输出，即那些可以通过测量知道的东西。
以下小节将更详细地讨论这些概念。

数学代写|matlab代写|Dynamic Coefficient Matrices and Input Coupling Matrices

X˙(吨)=dd吨X(吨) =F(吨)X(吨)+C(吨)在(吨)

F(吨)=[F11(吨)F12(吨)F13(吨)⋯F1n(吨) F21(吨)F22(吨)F23(吨)⋯F2n(吨) F31(吨)F32(吨)F33(吨)⋯F3n(吨) ⋮⋮⋮⋱⋮ Fn1(吨)Fn2(吨)Fn3(吨)⋯Fnn(吨)] C(吨)=[C11(吨)C12(吨)C13(吨)⋯C1r(吨) C21(吨)C22(吨)C23(吨)⋯C2r(吨) C31(吨)C32(吨)C33(吨)⋯C3r(吨) ⋮⋮⋮⋱⋮ Cn1(吨)Cn2(吨)Cn3(吨)⋯Cnr(吨)] 在(吨)=[在1(吨)在2(吨)在3(吨)⋯在r(吨)]吨

数学代写|matlab代写|Difference Equations and State Transition Matrices

X(吨ķ+1)−X(吨ķ)=ψ(吨ķ,X(吨ķ),在(吨ķ))

X(吨ķ+1)=φ(吨ķ,X(吨ķ),在(吨ķ)), φ(吨ķ,X(吨ķ),在(吨ķ))=X(吨ķ)+ψ(吨ķ,X(吨ķ),在(吨ķ)).

X(吨ķ+1)−X(吨ķ)=Ψ(吨ķ)X(吨ķ)+C(吨ķ)在(吨ķ), Xķ+1=披ķXķ+Cķ在ķ, 披ķ=一世+Ψ(吨ķ),

有限元方法代写

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MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。