Fixed-time stability criteria and adaptive state constrained control for uncertain switched nonlinear systems ☆

This paper investigates adaptive fixed-time state constrained tracking control problem for uncertain switched nonlinear systems, even if the fixed-time tracking control problem for each subsystem is not solvable. Based on the given fixed-time stability conditions, fixed-time stability criterion is established for switched nonlinear systems by developing a new multiple Lyapunov functions method. Then, by combining the fixed-time stability criterion with multiple integral barrier Lyapunov functions, the fuzzy adaptive controllers and a switching law dependent on states are designed constructively to solve the constrained fixed-time tracking control problem: 1) the boundedness of all the signals of the resulting closed-loop system is verified; 2) the system output can follow a given reference signal into an arbitrarily small compact set; 3) all the system states satisfy with their constraint condition. Finally, two examples are presented to verify the effectiveness of the obtained results.