Optimal exponential feedback stabilization of planar systems

Abstract

This paper solves the problem of finding an optimal feedback control ensuring the maximal rate of convergence of system solutions to the origin for a general class of planar control systems including switched, bilinear systems and ones described by differential inclusions, etc. The prescribed control set is assumed to be compact but not necessarily convex. The developed approach is based on finding the minimal Lyapunov exponent of the system with an open loop control which provides an upper bound for the optimal convergence rate of the closed loop system. Then an optimal feedback controller is constructed for which the obtained bound is attained.