Fixed-time control of nonlinear discrete-time systems with time-varying delay and uncertain parameters: state and output feedback approaches

This paper presents robust fixed-time controllers for nonlinear discrete-time systems with time-varying delay and uncertain parameters. The nonlinear function has the Lipschitz condition, and the uncertain parameters are time-varying. Firstly, by selecting an appropriate Lyapunov-Krasovskii functional, sufficient conditions are extracted to guarantee the fixed-time boundedness in the presence of uncertain parameters and external disturbance. To obtain the state feedback controller gain, these sufficient conditions are presented in the form of linear matrix inequalities. Secondly, output feedback is employed to solve the problem in the presence of uncertain parameters. The effectiveness of the proposed method is also illustrated through two examples.