Symmetry-Based Control and State Estimation of Nonlinear Systems in Prescribed Time

In this paper, we design novel types of smooth time-varying controllers/observers for lower triangular nonlinear systems with prescribed time convergence. We prove the results under very mild conditions: No global restrictions or bounds on the nonlinearities are required, but only locally Lipschitz conditions or the existence of solutions over finite intervals. Our smooth time-varying controllers/observers have completely different features in comparison with traditional homogenous or sliding-mode controllers/observers and existing smooth time-varying controllers/observers, being designed with a symmetry-based strategy.