Restriction of Control Systems

Abstract

Let us consider the affine control system

$$\dot y = {f_0}(y) + f(y)u,y \in M \subset {R^n},u \in {R^r}$$

which is an object S in the category AS. In the terminology of the theory of categories (see Sec. 1.2), a subobject of the object S is a pair consisting of an affine control system

$$\dot x = {h_0}(x) + h(x)v,x \in L \subset {R^m},v \in {R^s}$$

which is an object $\tilde s$ in the category AS, and a monomorphism, i.e., a morphism v: L → M that is an injection. System (5.2) is called a subsystem of system (5.1).