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

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 $u\in {\Omega }_j\subset R$ for x∈G j . The controllability function method is used to construct the feedback control.