Feedback Control Design for Systems with x-Discontinuous Right-Hand Side

Abstract

The problem of the admissible feedback synthesis for nonlinear systems with discontinuous right-hand side is considered. Sufficient conditions for solvability of this problem are proved. The neighborhood of the origin is broken in a finite number of domains G 1,G 2,…,G k . In each G j a control system $\dot{x}=f_{j}(x,u)$ is given. The problem of the admissible feedback synthesis is completely studied for control systems of the form $\dot{x}=a_{j}(x)+\gamma_{j}(x,u) b_{j}(x)$ , where $u\in \Omega_{j} \subset \Bbb{R}$ for x∈G j . The controllability function method is used to construct the feedback control.