Categories of Control Systems

Abstract

In this chapter, we study nonlinear control systems of the type

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

where f ₀ is a smooth vector field, f is an n × r-matrix whose columns f _α , α = l,...,r, are smooth vector fields, and M is a domain in ℝⁿ, called the phase space of the system. The variables y are called the phase variables, and u are the controls.