Nonsmooth feedback stabilization of a class of nonlinear systems with unknown control direction and time delay

Abstract

Summary The problem of global stabilization by nonsmooth state feedback is investigated for a family of time‐delay nonlinear systems with unknown control direction. Using the idea of the Nussbaum function from universal control, we present a delay‐free, nonsmooth dynamic state feedback strategy to achieve asymptotic state regulation with boundedness of the closed‐loop system. The proposed control scheme allows one to design a set of Lyapunov‐Krasovskii functionals and nonsmooth dynamic compensators simultaneously, by the technique of adding a power integrator. It is shown that while the effects of unknown control direction can be mitigated by the Nussbaum‐type gains, the strong nonlinearity with time delay can be effectively dealt with by nonsmooth state feedback controllers whose gains are updated dynamically.