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

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.