Criteria of the functional controllability and invertibility of non-linear systems (Q2714643)

The author considers the nonlinear controllable system NEWLINE\[NEWLINE \begin{aligned} \dot x &= f(t,x,u),\\ y &= h(t,x,u), \end{aligned}\tag{1} NEWLINE\]NEWLINE where \(x\in D\subseteq \mathbb{R}^n\), \(u\in U\subseteq \mathbb{R}^m\), \(t\in T=[0,t_1]\subseteq [0,\infty)\), \(y\in Y\subseteq \mathbb{R}^k\) is an output vector. The conditions of functional controllability and invertibility of system (1) are established. The obtained conditions are illustrated by examples of second and third order systems.