Barrier Lyapunov functions for the output tracking control of constrained nonlinear switched systems

In this paper, we investigate the output tracking control problem of constrained nonlinear switched systems in lower triangular form. First, when all the states are subjected to constraints, we employ a Barrier Lyapunov Function (BLF), which grows to infinity whenever its arguments approach some finite limits, to prevent the states from violating the constraints. Based on the simultaneous domination assumption, we design a continuous feedback controller for the switched system, which guarantees that asymptotic output tracking is achieved without transgression of the constraints and all closed-loop signals remain bounded, provided that the initial states are feasible. Then, we further consider the case of asymmetric time-varying output constraints by constructing an appropriate BLF. Finally, the effectiveness of the proposed results is demonstrated with a numerical example.