L2$$ {L}_2 $$‐gain analysis and fault‐tolerant control for nonlinear discrete‐time switched systems with time‐varying delay and actuator saturation

The ‐gain analysis and fault‐tolerant control of a class of uncertain nonlinear discrete‐time switched systems with time‐varying delay and actuator saturation are studied by using the multiple Lyapunov functions method. The fault‐tolerant state feedback controllers and the switching law are designed such that the closed‐loop system with actuator failures satisfies the disturbance attenuation performance indicator. The problem of estimating the capacity of admissible disturbance is transformed into a constrained optimization problem to ensure that the state trajectory of the closed‐loop system is bounded under the action of external disturbances. The upper bound of restricted ‐gain is estimated by solving constrained optimization problems. Then, when the fault‐tolerant controller can be regard as the design variable, the optimization problems above are adjusted for solving control synthesis problems. Finally, the numerical example is given to verify the effectiveness of the design method.