Representing a nonlinear input-output differential equation as an input-state-output system
Representing a nonlinear input-output differential equation as an input-state-output system
复制标题
将非线性输入-输出微分方程表示为输入-状态-输出系统
DOI：
10.1007/978-1-4471-0807-8_45
复制
发表时间：
1999
影响因子：
1.1
通讯作者：
A. Schaft
中科院分区：
文献类型：
--
作者：
A. Schaft
众所周知，每个高阶线性微分方程组
$${P_0}y+{P_1}\点y+\ldots+{P_k}{y^{\Left(k\Right)}}={Q_0}u+{Q_1}\点u+\ldots+{Q_k}{u^{\Left(k\Right)}}$$
(45.1)
其中y∈ℝp，u∈ℝm，P(S)：=P0+P1 S+…+P k S k a p×p多项式矩阵的判定P(S)≢0，可用极小状态空间系统来表示(实现
$$\Begin{ARRAY}{L}\Dot x=Ax+Bu，\；x\in{^n}\\y=Cx+Du\end{ARRAY}$$
(45.2)
It is well-known that every linear system of higher-order differential equations
$${P_0}y + {P_1}\dot y + \ldots + {P_k}{y^{\left( k \right)}} = {Q_0}u + {Q_1}\dot u + \ldots + {Q_k}{u^{\left( k \right)}}$$
(45.1)
with y ∈ ℝ p ,u ∈ ℝ m , and P(s):= P 0 + P 1 s + … + P k s k a p × p polynomial matrix with det P(s) ≢ 0, can be represented (realized) by a minimal state space system
$$\begin{array}{l} \dot x = Ax + Bu,\; x \in {^n}\\ y = Cx + Du \end{array}$$
(45.2)