7 非线性控制系统的几何理论 7.1 非线性控制系统的几何描述 定义在R~n上的一般非线性系统可以用微分方程描述如下: x=f(x,4) (7.1a) y=h(x) (7.1b)这里,状态x∈R~n;控制u∈R~m;输出y∈R~r,等式(7.1a)称为状态方程,(7.1b)称为输出方程。为了便于使用微分几何的工具,假设f对x和u都是光滑或解析函数,同样,h(x)也是C~∞ 7. THEORY OF NONLINEAR CONTROL SYSTEMS 7.1. Geometric Description of Nonlinear Control Systems General nonlinear systems defined on R ~ n can be described by differential equations as follows: x = f (x, 4) (7.1a) y = h (7.1b) Here, the state x∈R ~ n; control u∈R ~ m; output y∈R ~ r, equation (7.1a) is called the state equation, (7.1b) is called the output equation. In order to facilitate the use of differential geometry tools, assuming that f is a smooth or analytic function for both x and u, similarly, h (x) is also C ~ ∞